Search results for ""Author Laurent Decreusefond""

This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all the results which are known even for the basic subjects which are addressed here. The goal was to give the largest possible variety of proof techniques. For instance, we did not focus on the proof of concentration inequality for functionals of the Brownian motion, as it closely follows the lines of the analog result for Poisson functionals. This book grew from the graduate courses I gave at Paris-Sorbonne and Paris-Saclay universities, during the last few years. It is supposed to be as accessible as possible for students who have knowledge of Itô calculus and some rudiments of functional analysis.

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This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems. The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an ergodic theoretical perspective is also provided, as well as spatial point processes. Using these basic tools, stability criteria, performance measures and comparison principles are obtained for a wide class of models, from the canonical M/M/1 and G/G/1 queues to more sophisticated systems, including the current “hot topics” of spatial radio networking, OFDMA and real-time networks. Contents 1. Introduction. Part 1: Discrete-time Modeling 2. Stochastic Recursive Sequences. 3. Markov Chains. 4. Stationary Queues. 5. The M/GI/1 Queue. Part 2: Continuous-time Modeling 6. Poisson Process. 7. Markov Process. 8. Systems with Delay. 9. Loss Systems. Part 3: Spatial Modeling 10. Spatial Point Processes.

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