Description
Book SynopsisAlso called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus.
From the reviews:
"Introduction to Stochastic Integration is exactly what the title says.
Trade ReviewFrom the reviews:
"This textbook is a self-contained and systematic introduction to Itô’s stochastic integration with respect to martingales. The author gives special emphasis to the Brownian motion case. … Exercises are given in each chapter." (Jorge A. León, Mathematical Reviews, Issue 2006 e)
"Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents. … Given its clear structure and composition, the book could be useful for a short course on stochastic integration. The concepts are easy to grasp … . Problems are given in each chapter and naturally are proof-based." (Ita Cirovic Donev, The Mathematical Sciences Digital Library, June, 2006)
"This is a very good book on stochastic integration covering subjects from a construction of a Brownian motion to stochastic differential equations. It grew up from lecture notes the author elaborated during several years, and can be equally well used for teaching and self-education. The text is extremely clear and concise both in language and mathematical notation. Every topic is illustrated by simple and motivating examples. … is a timely, happily designed and well written book. It will be useful for unprepared and advanced readers." (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1101 (3), 2007)
"This book covers stochastic integration with respect to square-integrable martingales. … I am sure that this book will be very welcomed by students and lectures of this subject … who will find many illustrative exercises provided. Reader also should not miss out on the Preface, which includes some anecdotes about K. Itô." (Thorsten Rheinländer, Journal of the American Statistical Association, Vol. 103 (483), September, 2008)
Table of ContentsBrownian Motion.- Constructions of Brownian Motion.- Stochastic Integrals.- An Extension of Stochastic Integrals.- Stochastic Integrals for Martingales.- The Itô Formula.- Applications of the Itô Formula.- Multiple Wiener-Itô Integrals.- Stochastic Differential Equations.- Some Applications and Additional Topics.
