Stochastic Processes, 1st ed. 2017 Probability and Its Applications Series

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.

Gives a rigorous yet understandable presentation of the theory of stochastic processes

Presents the theory of distributions of functionals of diffusions including local times, rarely found in literature

Devotes serious attention to the Brownian local time

Includes many examples and exercises

Includes supplementary material: sn.pub/extras