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.

• 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.