Hybrid Switching Diffusions

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.

Chapter 1 Introduction and Motivation. - Chapter 2 Switching Diffusion. - Chapter 3 Recurrence. - Chapter 4 Ergodicity. - Chapter 5 Numerical Approximation. - Chapter 6 Stability. - Chapter 7 Stability of Switching ODEs. - Chapter 8 Invariance Principles. - Chapter 9 Two-Time-Scale Switching Diffusions. - Chapter 10 Switching Jump Diffusions: Time-Scale Separations. - Chapter 11 Past-Dependent Switching Diffusion. - Chapter 12 Population Dynamics Modeled by Switching Diffusion. - Appendix. - References. - Index.