Stochastic Analysis and Diffusion Processes

Paperback | January 7, 2014

byGopinath Kallianpur, P. Sundar

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Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of StochasticAnalysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details.Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Ito formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) whicharise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book.The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such asinvariant measures, ergodic behavior, and large deviation principle for diffusions.Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interestedin stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.

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From the Publisher

Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of StochasticAnalysis, and probabilistic behavior of diffusion...

Gopinath Kallianpur, Professor Emeritus at University of North Carolina at Chapel Hill, has worked extensively on Stochastic Analysis and is a world renowned expert on stochastic filtering theory. He is the author of Stochastic Filtering Theory, and a co-author of White Noise Theory of Prediction, Filtering and Smoothing, Introduction...

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Format:PaperbackDimensions:368 pages, 9.21 × 6.14 × 0.01 inPublished:January 7, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199657076

ISBN - 13:9780199657070

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Table of Contents

1. Introduction to Stochastic Processes2. Brownian Motion and Wiener Measure3. Elements of Martingale Theory4. Analytic Tools for Brownian Motion5. Stochastic Integration6. Stochastic Differential Equations7. The Martingale Problem8. Probability Theory and Partial Differential Equations9. Gaussian Solutions10. Jump Markov Processes11. Invariant Measures and Ergodicity12. Large Deviations for Diffusions