Stochastic Processes (Probability and Its Applications)

This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.-- Provided by publisher Front Matter ....Pages i-xiv Basic Facts (Andrei N. Borodin)....Pages 1-84 Stochastic Calculus (Andrei N. Borodin)....Pages 85-196 Distributions of Functionals of Brownian Motion (Andrei N. Borodin)....Pages 197-266 Diffusion Processes (Andrei N. Borodin)....Pages 267-358 Brownian Local Time (Andrei N. Borodin)....Pages 359-438 Diffusions with Jumps (Andrei N. Borodin)....Pages 439-500 Invariance Principle for Random Walks and Local Times (Andrei N. Borodin)....Pages 501-582 Back Matter ....Pages 583-626