Stochastic Analysis and Diffusion Processes
Series: Oxford Graduate Texts in Mathematics; 24;
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Product details:
- Publisher OUP Oxford
- Date of Publication 9 January 2014
- ISBN 9780199657070
- Binding Paperback
- No. of pages368 pages
- Size 234x156 mm
- Weight 556 g
- Language English 0
Categories
Short description:
Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.
MoreLong description:
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 Stochastic Analysis, 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 Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise 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 as invariant 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 interested in 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.
Very readable
Table of Contents:
Introduction to Stochastic Processes
Brownian Motion and Wiener Measure
Elements of Martingale Theory
Analytic Tools for Brownian Motion
Stochastic Integration
Stochastic Differential Equations
The Martingale Problem
Probability Theory and Partial Differential Equations
Gaussian Solutions
Jump Markov Processes
Invariant Measures and Ergodicity
Large Deviations for Diffusions
