Mathematical models in physics, engineering, biology, finance theory, and other fields are inherently stochastic rather than deterministic. Stochastic analysis provides the mathematics needed to understand any evolving phenomenon in the face of uncertainties. Stochastic Analysis and Diffusion Processes presents a simple, coherent introduction to stochastic calculus.
This book starts right from the concept of random processes and Brownian motion and builds the theory and research directions in a self-contained manner. The book grew out of the authors' lecture notes developed for teaching stochastic analysis over a number of years.
Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter. 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.
1: Introduction to Stochastic Processes 2: Brownian Motion and Wiener Measure 3: Elements of Martingale Theory 4: Analytic Tools for Brownian Motion 5: Stochastic Integration 6: Stochastic Differential Equations 7: The Martingale Problem 8: Probability Theory and Partial Differential Equations 9: Gaussian Solutions 10: Jump Markov Processes 11: Invariant Measures and Ergodicity 12: Large Deviations for Diffusions
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 to Option Pricing Theory, and Stochastic Differential Equations in Infinite Dimensions. P. Sundar is a Professor of Mathematics at Louisiana State University. He works on Stochastic Analysis, and is on the Editorial Board for the journal Communications on Stochastic Analysis. He has co-edited a book titled Infinite Dimensional Stochastic Analysis.
Reviews for Stochastic Analysis and Diffusion Processes
The book can be recommended for all specialists in probability and stochastic processes and its applications starting from the undergraduate and graduate students and ending with experienced professionals. * Yuliya S. Mishura, Zentralblatt MATH * If I were giving a graduate course on this topic, then I would certainly use this book. * Dave Applebaum, The Mathematical Gazette * Very readable * Paul Taylor, Mathematics Today *