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.

  Autorentext

  Hai-Dang Nguyen received the B.S. degree in mathematics from the VNU, Hanoi University of Science, Hanoi, Vietnam, in 2008, and the Ph.D. in applied mathematics from Wayne State University, Detroit, MI, USA, in 2018. He joined the University of Alabama, Tuscaloosa, AL, USA, in 2018 as an Assistant Professor and was promoted to Associate Professor, in 2022. His research interests include stochastic systems and applications, mathematical biology, and stochastic control. Dr. Nguyen was the recipient of SIAM Activity Group on Control and Systems Theory Prize in 2019. He is an Associate Editor of Nonlinear Analysis: Hybrid Systems and SIAM Journal on Control and Optimization.

  George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, the M.S. degree in electrical engineering, and the Ph.D. degree in applied mathematics from Brown University in 1987. He joined the Department of Mathematics, Wayne State University in 1987, and became Professor in 1996 and University Distinguished Professor in 2017. He moved to the University of Connecticut in 2020. He was the Editor-in-Chief of SIAM Journal on Control and Optimization from 2018-2023, and is/was on editorial board of many other journals. He is a Fellow of IEEE, a Fellow of IFAC, and a Fellow of SIAM.

  Chao Zhu received his B.S. and M.S. degrees in mathematics from East China Normal University, Shanghai, China, in 1999 and 2002, respectively, and his Ph.D. in mathematics from Wayne State University in 2007, under the supervision of Prof. George Yin. He joined the Department of Mathematical Sciences, the University of Wisconsin Milwaukee in 2007 and became a Professor in 2018. He is currently serving on the editorial boards of three journals. His research interests include stochastic analysis, and stochastic control and their applications in areas such as mathematical nance, mathematical biology, and risk management.