Stochastics Books

Book SynopsisThis book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models.The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.Trade Review"Introductory facts related to weak convergence of the stochastic process and the convergence of semimartigales, theorems, generalizations for results previously published by the authors, proofs and applications are well organized and distributed throughout nine chapters and three appendices."Mathematical Reviews"This book may serve as a textbook for graduate students, postdoctoral seminars or courses for applied scientists and engineers in stochastic approximation of complex systems: queueing, reliability, risk, finance."Zentralblatt MATHTable of ContentsMarkov and Semi-Markov Processes Stochastic Systems with Switching Stochastic Systems in the Series Scheme Stochastic Systems with Split and Merging Phase Merging Principles Weak Convergence Poisson Approximation Applications Appendices: Weak Convergence of Probability Measures Some Limit Theorems for Stochastic Processes Some Auxiliary Results

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Book SynopsisThis volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very highest quality papers in the field of financial mathematics.Table of ContentsFinancial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy (S Ankirchner & P Imkeller); Model-Free Representation of Pricing Rules as Conditional Expections (S Biagini & R Cont); Risky Debt and Optimal Coupon Policy and Other Optimal Strategies (D Dorobantu & M Pontier); The Investment Game Under Uncertainty: An Analysis of Equilibrium Values in the Presence of First or Second Mover Advantage (J Imai & T Watanabe); Cubature on Wiener Continued (C Litterer & T Lyons); Numerical Approximation by Quantization for Optimization Problems in Finance Under Partial Observations (H Pham); and other papers.

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Book SynopsisThis book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.Table of ContentsEquilibrium Statistical Mechanics: General Principles of Many-Particle Systems; Classical and Quantum Formalisms. The Boltzmann Gas, the Perfect Bose Gas and Fermi Gas; Quantum Systems with Strong Interactions; Non-Equilibrium Statistical Mechanics: Classical Transport Theory; Linear Response Theory and Quantum Transport; Stochastic Phenomena; Appendices: The Schrodinger, Heisenberg and Interaction Pictures; Spin and Statistics.

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Book SynopsisMost introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.Table of ContentsA Review of Probability Distributions and Their Properties; Definition and Characteristics of a Stochastic Process; Some Important Classes of Stochastic Processes; Stationary Processes; The Brownian Motion and the Poisson Process, Levy Processes; Renewal Processes and Random Walks; Martingales in Discrete Time; Branching Processes; Regenerative Phenomena; Markov Chains; Tauberian Theorems.

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Book SynopsisThis volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations.The other papers in this volume were specially written for the occasion of Prof Rozovskii's 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives.Table of ContentsStochastic Evolution Equations (N V Krylov & B L Rozovskii); Predictability of the Burgers Dynamics Under Model Uncertainty (D Blomker & J Duan); Asymptotics for a Space-Time Wigner Transform (L Borcea et al.); KdV Equation with Homogeneous Multiplicative Noise (A de Bouard & A Debussche); Stochastic Fractional Burgers Equation (Z Brze niak & L Debbi); Optimal Compensation of Executives (A Cadenillas et al.); The Freidlin-Wentzell LDP with Rapidly Growing Coefficients (P Chigansky & R Liptser); Convergence Rate of Weak Approximations (D Crisan & S Ghazali); Flow Properties of SDEs Driven by Fractional Brownian Motion (L Decreusefond & D Nualart); Regularity for Stochastic Navier-Stokes Equation (F Flandoli & M Romito); Rate of Convergence of Implicit Approximations (L Gyongy & A Millet); Maximum Principle for SPDEs (N V Krylov); Delay Estimation for Diffusion Processes (Yu A Kutoyants); Cauchy-Dirichlet Problem for an Integro-Differential Equation (R Mikulevicius & H Pragarauskas); Strict Solutions of Kolmogorov Equations (G Da Prato).

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Book SynopsisThis volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).Table of ContentsRandom Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals.

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Book SynopsisThe ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.Table of ContentsStochastic Parallel Transport on the d-Dimensional Torus (A B Cruzeiro & P Malliavin); Riemannian Geometry of Diff(S1)/S1 Revisited (M Gordina); Ergodic Theory of SDEs with Degenerate Noise (A Kupiainen); Dynkin's Isomorphism without Symmetry (Y Le Jan); Large Deviations for the Two-Dimensional Yang-Mills Measure (T Levy); Laplace Operator in Networks of Thin Fibers: Spectrum Near the Threshold (S Molchanov & B Vainberg); Adiabatic Limits and Quantum Decoherence (R Rebolledo & D Spehner); Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects (A N Sengupta); Near Extinction of Solution Caused by Strong Absorption on a Fine-Grained Set (V V Yurinsky & A L Piatnitski).

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Book SynopsisOperations research uses quantitative models to analyze and predict the behavior of systems and to provide information for decision makers. Two key concepts in such research are optimization and uncertainty. Typical models in stochastic operations research include queueing models, inventory models, financial engineering models, reliability models, and simulation models. This book contains a collection of peer-reviewed papers from the International Workshop on Recent Advances in Stochastic Operations Research (2007 RASOR Nanzan) held on March 5-6, 2007, at Nanzan University, Nagoya, Japan. It enables advanced readers to understand the recent topics and results in stochastic operations research.

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Book SynopsisThe book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.Table of ContentsFoundations of Markov Random Walks and Markov Additive Processes: Theory of Semiregenerative Phenomena; Markov Random Walk-Fluctuation Theory and Wiener-Hopf Factorization; Further Results for Semiregenerative Phenomena; Limits Theorems for Markov Random Walks; Markov Renewal and Markov-Additive Processes -- A Review and Some New Results; Markov-Additive Processes of Arrivals; Application Examples: Markov-Modulated Single-Server Queueing Systems; A Storage Model for Data Communications Systems; A Markovian Storage Model.

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Book SynopsisThis textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.

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Book SynopsisThis book contains the general description of the mathematical pendulum subject to constant torque, periodic and random forces. The latter appear in additive and multiplicative form with their possible correlation. For the underdamped pendulum driven by periodic forces, a new phenomenon — deterministic chaos — comes into play, and the common action of this chaos and the influence of noise are taken into account. The inverted position of the pendulum can be stabilized either by periodic or random oscillations of the suspension axis or by inserting a spring into a rigid rod, or by their combination. The pendulum is one of the simplest nonlinear models, which has many applications in physics, chemistry, biology, medicine, communications, economics and sociology. A wide group of researchers working in these fields, along with students and teachers, will benefit from this book.Table of ContentsFormulation of the Problem; Deterministic Motion; Underdamped Pendulum; Deterministic Chaos; Inverted Pendulum.

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Book Synopsis'The book remains a valuable tool both for statisticians who are already familiar with the theory of copulas and just need to develop sampling algorithms, and for practitioners who want to learn copulas and implement the simulation techniques needed to exploit the potential of copulas in applications.'Mathematical ReviewsThe book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.

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Book SynopsisWhy should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by 'time'. And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman 'integral', wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's 'integral' can now be understood, the 'It's all in the vacuum' ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume.Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise.The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.

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Book SynopsisRandom processes are one of the most powerful tools in the study and understanding of countless phenomena in natural and social sciences.The book is a complete medium-level introduction to the subject. The book is written in a clear and pedagogical manner but with enough rigor and scope that can appeal to both students and researchers.This book is addressed to advanced students and professional researchers in many branches of science where level crossings and extremes appear but with some particular emphasis on some applications in socio-economic systems.

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Book SynopsisThe book is devoted to limit theorems for nonconventional sums and arrays. Asymptotic behavior of such sums were first studied in ergodic theory but recently it turned out that main limit theorems of probability theory, such as central, local and Poisson limit theorems can also be obtained for such expressions. In order to obtain sufficiently general local limit theorem, we develop also thermodynamic formalism type results for random complex operators, which is one of the novelties of the book.

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Book SynopsisStochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also to scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.Table of ContentsIntroduction: Stochastic Analysis and Stochastic Dynamics; A Glimpse of Stochastic Dynamical Systems; Progress in White Noise Analysis; Dynamical Systems Driven by Fractional Brownian Motion; Dynamical Systems Driven by Non-Gaussian Noise; Stochastic Dynamical Systems with Memory; Simulation of Stochastic Dynamical Systems.

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Book SynopsisThe book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.Table of ContentsIntroduction: Introduction: Stochastic Differential Equations; Strong Markov Processes: Strong Markov Processes on Polish Spaces; Strong Markov Processes: Proof on Main Results; Space-Time Operators and Miscellaneous Topics; Backward Stochastic Differential Equations: Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes; Viscosity Solutions, Backward Stochastic Differential Equations and Markov Processes; The Hamilton-Jacobi-Bellman Equation and the Stochastic Noether Theorem; Long Time Behavior: On Non-Stationary Markov Processes and Dunford Projections; Coupling Methods and Sobolev Type Inequalities; Invariant Measure.

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Book SynopsisChange of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. It is invaluable as a textbook for graduate-level courses and students or a handy reference for researchers and practitioners in financial mathematics and econometrics.Table of ContentsRandom Change of Time; Integral Representations and Change of Time in Stochastic Integrals; Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis; Stochastic Exponential and Stochastic Logarithm. Cumulant Processes; Processes with Independent Increments. Levy Processes; Change of Measure. General Facts; Change of Measure in Models Based on Levy Processes; Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes; Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case; Martingale Measures in the Stochastic Theory of Arbitrage; Change of Measure in Option Pricing; Conditionally Brownian and Levy Processes. Stochastic Volatility Models.

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Book SynopsisThis volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.Table of ContentsExistence of the Fock Representation for Current Algebras of the Galilei Algebra (L Accardi et al.); Modular Structures and Landau Levels (F Bagarello); On Spectral Approach to Pascal White Noise Functionals (A Barhoumi); Spectral Analysis for Twisted Waveguides (P Briet); Classification of Invarient State of Generic Quantum Markov Semigroups: The Gaussian Gauge (S Hachiha); On Difficulties Appearing in the Study of Stochastic Volterra Equations (A Karczewska); Entanglement Protection and Generation in Two Atom System (M Orszag); Hilbert Molecules - Square Roots of Positive Maps (M Skeide); Multiparameter Quantum Stochastic Processes (J Spring); and other papers.

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Book SynopsisThis book introduces some advanced topics in probability theories — both pure and applied — is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.Table of ContentsStochastic Analysis and Systems: Multidimensional Wick-Ito Formula for Gaussian Processes (D Nualart & S Ortiz-Latorre); Fractional White Noise Multiplication (A H Tsoi); Invariance Principle of Regime-Switching Diffusions (C Zhu & G Yin); Finance and Stochastics: Real Options and Competition (A Bensoussan et al.); Finding Expectations of Monotone Functions of Binary Random Variables by Simulation, with Applications to Reliability, Finance, and Round Robin Tournaments (M Brown et al.); Filtering with Counting Process Observations and Other Factors: Applications to Bond Price Tick Data (X Hu et al.); Jump Bond Markets Some Steps towards General Models in Applications to Hedging and Utility Problems (M Kohlmann & D Xiong); Recombining Tree for Regime-Switching Model: Algorithm and Weak Convergence (R H Liu); Optimal Reinsurance under a Jump Diffusion Model (S Luo); Applications of Counting Processes and Martingales in Survival Analysis (J Sun); Stochastic Algorithms and Numeries for Mean-Revertig Asset Trading (Q Zhang et al.).

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Book SynopsisThis book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.

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Book SynopsisThis book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on.Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves.Table of ContentsWeb Markov Skeleton Processes; Generalised Burgers Equations; Backward Stochastic Differential Equations (BSDEs) Driven by Fractional Brownian Motion; Measure Solutions of BSDEs with Generator of Quadratic Growth; Parameter Estimates of Drift Brownian Motion; Spectral Bounds on Feymann - Kac Semigroups; Stochastic Analysis on Lie Group; Potential Theory of Subordinate Brownian Motion; Stochastic Control of Stochastic Partial Differential Equations with Delay; and other papers.

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Book SynopsisInterest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.Table of ContentsA Review of Stochastic Calculus; A Review of Black - Scholes Pricing; Short Term Interest Rate Models; Pricing of Zero-Coupon Bonds; Forward Rate Modeling; The Heath - Jarrow - Morton (HJM) Model; The Forward Measure and Derivative Pricing; Curve Fitting and a Two Factor Model; A Credit Default Model; Pricing of Caps and Swaptions on the LIBOR; The Brace - Gatarek - Musiela (BGM) Model; Mathematical Tools; Some Recent Developments; Solutions to the Exercises.

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Book SynopsisThis book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop several state space models for many genetic problems, carcinogenesis and other biomedical problems.To emphasize special applications to medical problems, in this new edition the book has added a new chapter to illustrate how to develop biologically-supported stochastic models and state space models of carcinogenesis in human beings. Specific examples include hidden Markov models and state space models for human colon cancer, human liver cancer and some human pediatric cancers such as retinoblastoma and hepatoblastoma. The book also gives examples to illustrate how to develop procedures to assess cancer risk of environmental agents through initiation-promotion protocols.Table of ContentsDiscrete Time Markov Chain Models in Genetics and Biomedical Systems; Stationary Distributions and MCMC in Discrete Time Markov Chains; Continuous-Time Markov Chain Models in Genetics, Cancers and AIDS; Absorption Probabilities and Stationary Distributions in Continuous-Time Markov Chain Models; Diffusion Models in Genetics, Cancer and AIDS; Asymptotic Distributions, Stationary Distributions and Absorption Probabilities in Diffusion Models; State Space Models and Some Examples from Cancer and AIDS; Some General Theories of State Space Models and Applications.

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Book SynopsisThis book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.Trade ReviewLike its predecessor volumes, this conference proceedings is an up-to-date record of the current status of the maturing field of stochastic programming. Its advance is supported here by articles which report on practical applications in finance, production, logistics, energy and telecommunications. -- M A H Dempster "Professor Emeritus, Center for Financial Research, Department of Pure Mathematics and Statistics, University of Cambridge & Cambridge Systems Associates Limited, Cambridge UK"Table of ContentsFinance: Longevity Risk Management for Individual Investors; Optimal SP-Based Personal Financial Planning with Intermediate and Long Term Goals; Intertemporal Surplus Management with Jump Risks; Jump-Diffusion Risk-Sensitive Benchmarked Asset Management; Dynamic Portfolio Optimization Under Regime-Based Firm Strength; Options Portfolio Management as a Chance Constrained Problem; Stochastic Models for Optimizing Immunization Strategies in Fixed-Income Security Portfolios Under Some Sources of Uncertainty; Stochastic Programming and Optimization in Horserace Betting; Production Planning and Logistics: Multi-Stage Stochastic Programming for Natural Gas Infrastructure Design with a Production Perspective; Stochastic Programming Model for Optimizing the Production of Farmed Atlantic Salmon; Prioritizing Network Interdiction of Nuclear Smuggling; Sawmill Production Planning Under Uncertainty: Modelling and Solution Approaches; Energy: An Electricity Procurement Model with Energy and Peak Charges; Value of Flexibility in Hydroelectric Reservoir Operations; Multi-Lag Benders Decomposition for Power Generation Planning with Nonanticipativity Constraints on the Dispatch of LNG Thermal Plants; Theory Papers: Stochastic Second-Order Cone Programming in Mobile Ad-Hoc Networks; Stochastic Frequency Assignment Problem.

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Book SynopsisThis volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory.This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications.Tools and techniques presented here will be of great value to researchers.Table of ContentsCentral Extension of Virasoro Type Subalgebras of the Zamolodchikov - w∞ Lie Algebra (L Accardi and A Boukas); Entanglement Protection and Generation under Continuous Monitoring (A Barchielli and M Gregoratti); Completely Positive Transformations of Quantum Operations (G Chiribella, A Toigo and V Umanita); Invariant Operators in Schroedinger Setting (V K Dobrev); Generation of Semigroups by Degenerate Elliptic Operators Arising in Open Quantum Systems (F Fagnola and L Pantaleon Martinez); Quantum Observables on a Completely Simple Semigroup (Ph. Feinsilver); A Mathematical Treatment for the Contextual Dependent Bio-Systems (T Hara and M Ohya); On the Spectral Gap of the N-Photon Absorption-Emission Process (R Hermida and R Quezada); Some Recent Topics on White Noise Theory (T Hida and Si Si); Quantum Levy Area as a Quantum Martingale Limit (R L Hudson); On Computational Complexity of Quantum Algorithm for Factoring (S Iriyama, M Ohya and I V Volovich); Prequantum Classical Statistical Field Theory: Derivation of Gaussianity of Probability Distributions (A Khrennikov); A Survey on Extensions of Hilbert C*-Modules (B Kolarec); An Isometry Formula for a New Stochastic Integral (H H Kuo, A Sae-Tang and B Szozda); Infinite Dimensional Laplacians Associated with Derivatives of White Noise (K Saito); A New Noise Depending on a Space Parameter and Its Transformations (Si Si); Note on Complexities for Gaussian Communication Process (N Watanabe).

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Book SynopsisThe study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.Table of ContentsIntroduction to Superprocesses; Superprocesses in Random Environments; Linear SPDEs; Particle Representations for a Class of Nonlinear SPDEs; Stochastic Log-Laplace Equation; SPDEs for Density Fields of the Superprocesses in Random Environments; Backward Doubly Stochastic Differential Equations; From SPDEs to BSDEs.

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Book SynopsisStochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.Table of ContentsDiffusion Processes on Riemannian Manifolds; Reflecting Diffusion Processes on Riemannian Manifolds with Boundary; Coupling and Applications; Harnack Inequalities and Applications; Functional Inequalities and Applications; Formulae for the Curvature and Second Fundamental Form; Equivalent Semigroup Inequalities for the Lower Bounds of Curvature and Second Fundamental Form; Modified Curvature and Applications; Robin Semigroup and Applications; Stochastic Analysis on the Path Space Over Manifolds with Boundary; Subelliptic Diffusion Processes.

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Book SynopsisDiscrete event systems (DES) have become pervasive in our daily lives. Examples include (but are not restricted to) manufacturing and supply chains, transportation, healthcare, call centers, and financial engineering. However, due to their complexities that often involve millions or even billions of events with many variables and constraints, modeling these stochastic simulations has long been a “hard nut to crack”. The advance in available computer technology, especially of cluster and cloud computing, has paved the way for the realization of a number of stochastic simulation optimization for complex discrete event systems. This book will introduce two important techniques initially proposed and developed by Professor Y C Ho and his team; namely perturbation analysis and ordinal optimization for stochastic simulation optimization, and present the state-of-the-art technology, and their future research directions.Table of ContentsPart I: Perturbation Analysis: IPA Calculus for Hybrid Systems; Smoothed Perturbation Analysis: A Retrospective and Prospective Look; Perturbation Analysis and Variance Reduction in Monte Carlo Simulation; Adjoints and Averaging; Infinitesimal Perturbation Analysis in On-Line Optimization; Simulation-based Optimization of Failure-Prone Continuous Flow Lines; Perturbation Analysis, Dynamic Programming, and Beyond; Part II: Ordinal Optimization : Fundamentals of Ordinal Optimization; Optimal Computing Budget Allocation; Nested Partitions; Applications of Ordinal Optimization.

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Book SynopsisThis volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.Table of ContentsBrief Reminder of Probability Theory; Compound Poisson, Infinitely Divisible and Stable Random Variables; Gaussian Processes: Wiener Process, Fractional Brownian Motion, Etc.; Levy Processes; Uncorrelated and Independently Scattered Random Measures and Respective Integrals; Limit Theorems for Processes; Teletraffic Workload Models: Weak Dependence, Long Range Dependence, Gaussian, Stable, and Intermediate Limits; Kaj - Taqqu Telecom Processes; Multivariate Workload Models.

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Book SynopsisThis book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.Table of ContentsGaussian Measures on Infinite Dimensional Spaces; Hypergroups and Random Fields; A Concise Exposition of Large Deviations; Quantum White Noise Calculus and Applications; Weak Radon - Nikodym Derivatives, Dunford - Schwartz Type Integration, and Cramer and Karhunen Processes; Entropy, SDE - LDP and Fenchel - Legendre - Orlicz Classes; Bispectral Density Estimation in Harmonizable Processes.

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Book SynopsisThis is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation.The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Table of ContentsBasics of Probability Theory; Markov Chains; Markov Decision Processes; The Exponential Distribution and Poisson Process; Jump Markov Processes; Elements of Queueing Theory; Elements of Renewal Theory; Elements of Time Series; Elements of Stochastic Calculus; Elements of Mathematical Finance; Elements of Simulation.

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Book SynopsisThis is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation.The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Table of ContentsBasics of Probability Theory; Markov Chains; Markov Decision Processes; The Exponential Distribution and Poisson Process; Jump Markov Processes; Elements of Queueing Theory; Elements of Renewal Theory; Elements of Time Series; Elements of Stochastic Calculus; Elements of Mathematical Finance; Elements of Simulation.

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Book SynopsisThis book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of various eigenvalue statistics. This is attributed to the nice algebraic structures of models. This part also studies the Circular β Ensembles and Hermitian β Ensembles. Part III is devoted to the study of random uniform and Plancherel partitions. There is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models. A remarkable point is the conditioning argument in each model. Through enlarging the probability space, we run into independent geometric random variables as well as determinantal point processes with discrete Bessel kernels.This book treats only second-order normal fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes.

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Book SynopsisThis volume contains pedagogical, review and research level papers on fractional stochastic and quantum processes which have been the focus of intensive mathematical, experimental, and computational studies due to their widening spectrum of applications in natural and social sciences. Novel vis-à-vis standard approaches in fractional stochastic analysis are presented together with experimental and theoretical highlights in applications to single particle tracking, organic semiconductors, polymer structure, complex systems, and finance, among others.Table of ContentsAnomalous Diffusion Processes; Fractional Path Integrals; Fractional Brownian Motion and Polymers; Probing Cell Mechanics with Optical Tweezers; Diffusion of Alpha-Helical Proteins; Space Fractional Schrodinger Equation; Multifractional Processes; Path Summation with Memory; Grey Brownian Motion; Fractional Dynamics of Carrier Transport in Organic Semiconductors; Photostimulation of Neurons; Modeling Urban Dynamics;

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Book SynopsisStochastic descriptions of a harmonic oscillator can be obtained by adding additive noise, or/and three types of multiplicative noise: random frequency, random damping and random mass. The first three types of noise were intensively studied in many published articles. In this book the fourth case, that of random mass, is considered in the context of the harmonic oscillator and its immediate nonlinear generalization — the pendulum. To our knowledge it is the first book fully dedicated to this problem.Two interrelated methods, the Langevin equation and the Fokker-Planck equations, as well as the Lyapunov stability method are used for the mathematical analysis. After a short introduction, the two main parts of the book describe the different properties of the random harmonic oscillator and the random pendulum with random masses. As an example, the stochastic resonance is studied, where the noise plays an unusual role, increasing the applied weak periodic signal, and also the vibration resonance in dynamic systems, where the role of noise is played by the second high-frequency periodic signal.First and second averaged moments have been calculated for a system with different types of additive and multiplicative noises, which define the stability of a system. The calculations have been extended to two multiplicative noises and to quadratic noise. This book is useful for students and scientists working in different fields of statistical physics.Table of ContentsIntroduction; Oscillator with Random Mass; Pendulum with Random Mass;

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Book SynopsisThis volume provides more evidence against the Random Walk Hypothesis and offers insights into market inefficiency through systematically trading exchange-traded funds (ETFs). The book is organized to answer the following three questions: Do ETF prices follow random walks? If not, what are some of the factors that impact their non-random walk behavior? How can investors take advantage of such price dynamics in trading ETFs?Table of ContentsNon-Random Walk Behavior in ETF Price Dynamics; Variance Ratios; Equity, Bond, Commodity and Currency ETFs; Factors of Serial Correlation; Discretized Sampling of Variance and Volatility Trading;

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Book SynopsisChange of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.Table of ContentsRandom Change of Time; Integral Representations and Change of Time in Stochastic Integrals; Semimartingales: Basic Notions, Structures, Elements of Stochastic Analysis; Stochastic Exponential and Stochastic Logarithm. Cumulant Processes; Processes with Independent Increments. Levy Processes; Change of Measure. General Facts; Change of Measure in Models Based on Levy Processes; Change of Time in Semimartingale Models and Models Based on Brownian Motion and Levy Processes; Conditionally Gaussian Distributions and Stochastic Volatility Models for the Discrete-time Case; Martingale Measures in the Stochastic Theory of Arbitrage; Change of Measure in Option Pricing; Conditionally Brownian and Levy Processes. Stochastic Volatility Models; A Wider View. Ambit Processes and Fields, and Volatility/Intermittency;

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Book SynopsisThe goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.Table of ContentsA Few Introductory Problems; Basic Notions; Useful Stochastic Processes; Properties of Stochastic Processes; Stochastic Integration; Stochastic Differentiation; Stochastic Integration Techniques; Stochastic Differential Equations; Applications of Brownian Motion; Girsanov's Theorem and Brownian Motion; Some Applications of Stochastic Calculus; Hints and Solutions;

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Book SynopsisThe goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.Table of ContentsA Few Introductory Problems; Basic Notions; Useful Stochastic Processes; Properties of Stochastic Processes; Stochastic Integration; Stochastic Differentiation; Stochastic Integration Techniques; Stochastic Differential Equations; Applications of Brownian Motion; Girsanov's Theorem and Brownian Motion; Some Applications of Stochastic Calculus; Hints and Solutions;

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Book SynopsisStochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering.Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes.A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework.

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Book SynopsisThe objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.Table of ContentsDiscrete-Time Markov Chains; Continuous-Time Markov Chains; Reversible Markov Chains; General Markov Processes; Martingale; Brownian Motion; Stochastic Integral and Diffusion Processes; Semimartingale and Stochastic Integral;

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Book Synopsis

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Book Synopsis

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