About this book
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.
stochastic calculus diffusion processes Brownian motion differential equations conditional probabilities conditional expectations
“The aim of the book is to give a rigorous and at the same time accessible presentation of the theory of stochastic processes. … The book is written in a clear and rigorous language, and will be useful to students, graduate students, teachers and anyone who is interested in the theory of stochastic processes.” (Yuliya S. Mishura, zbMATH 1390.60003, 2018)