George Yin

This thoroughly revised and expanded edition presents a comprehensive study of hybrid switching diffusion processes and their wide-ranging applications. These processes, which combine continuous dynamics with discrete events, are essential for modeling complex systems influenced by random environments. They have broad applications in such fields as wireless communications, signal processing, queueing networks, production planning, ecosystems, financial engineering, and large-scale system optimization. Since the publication of the first edition, the study of hybrid switching diffusions has made significant strides, with new theoretical breakthroughs and emerging applications in ecology and population biology. This edition incorporates these advancements, refining and expanding several key chapters. Notably, it introduces a new chapter on switching processes with past dependence, extending the theoretical framework to account for historical states in the switching process.a new chapter on mathematical biology applications, demonstrating the relevance of hybrid switching diffusions in biological modeling. In addition to covering fundamental topics such as existence and uniqueness of solutions, recurrence, ergodicity, invariant measures, and stability, this edition further explores numerical methods and two-time-scale models. This book is an essential resource for applied mathematicians, probabilists, systems engineers, control scientists, operations researchers, and financial analysts. It is also well-suited for graduate courses on stochastic processes and hybrid systems. The new edition offers researchers and practitioners a robust and versatile framework, driving significant advancements and broadening the application of stochastic analysis to real-world challenges.

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.