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Stochastic Processes with Applications

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By Rabi N. Bhattacharya and Edward C. Waymire


2009 / xviii + 676 pages / Softcover / ISBN: 978-0-898716-89-4 / List Price $102.00 / SIAM Member Price $71.40 / Order Code CL61

Keywords: Markov processes, martingales, stochastic differential equations

"This may be the best all-around treatment [of stochastic processes] for use by graduate students with varied backgrounds but with some mathematical ambitions." 
– William G. Faris, University of Arizona

“The book is remarkably comprehensive. The additional notes at the end of the chapters contain a fund of information.” 
– Richard F. Gundy, Rutgers University

This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes.

The book features very broad coverage of the most applicable aspects of stochastic processes, including sufficient material for self-contained courses on

  • random walk in one and multiple dimensions; 
  • Markov chains in discrete and continuous times, including birth-death processes;
  • Brownian motion and diffusions; 
  • stochastic optimization; and 
  • stochastic differential equations.

This book can be used for a number of different courses for graduate students of mathematics, statistics, economics, engineering, and other fields who have some background in probability and analysis. It is also intended as a reference for researchers and professionals in many areas of science and technology whose work involves the application of probability.

Preface to the Classics Edition;
Sample Course Outline;
Chapter I: Random Walk and Brownian Motion;
Chapter II: Discrete-Parameter Markov Chains;
Chapter III: BirthÐDeath Markov Chains;
Chapter IV: Continuous-Parameter Markov Chains;
Chapter V: Brownian Motion and Diffusions;
Chapter VI: Dynamic Programming and Stochastic Optimization;
Chapter VII: An Introduction to Stochastic Differential Equations;
Chapter 0: A Probability and Measure Theory Overview;
Author Index;
Subject Index;

About the Authors
Rabi N. Bhattacharya is a Professor of Mathematics at the University of Arizona. He is an IMS Fellow, a member of the AMS, and a recipient of the Humboldt Prize and a Guggenheim Fellowship.

Edward C. Waymire is a Professor of Mathematics and Statistics at Oregon State University. He is a member of the AMS and SIAM, a Fellow of the IMS, and past Editor in Chief for the Annals of Applied Probability.

ISBN: 9780898716894

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