© 2010

Hybrid Switching Diffusions

Properties and Applications


  • Chapter summaries

  • Detailed Illustrations

  • Many worked out examples

  • Numerical Solutions

  • Applications to Finance


Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 63)

Table of contents

  1. Front Matter
    Pages 1-15
  2. G. George Yin, Chao Zhu
    Pages 1-24
  3. Basic Properties, Recurrence, Ergodicity

    1. Front Matter
      Pages 26-26
    2. G. George Yin, Chao Zhu
      Pages 27-67
    3. G. George Yin, Chao Zhu
      Pages 69-109
    4. G. George Yin, Chao Zhu
      Pages 111-134
  4. Numerical Solutions and Approximation

    1. Front Matter
      Pages 136-136
    2. G. George Yin, Chao Zhu
      Pages 137-157
    3. G. George Yin, Chao Zhu
      Pages 159-179
  5. Stability

    1. Front Matter
      Pages 182-182
    2. G. George Yin, Chao Zhu
      Pages 183-215
    3. G. George Yin, Chao Zhu
      Pages 217-250
    4. G. George Yin, Chao Zhu
      Pages 251-281
  6. Two-Time-Scale Modeling and Applications

    1. Front Matter
      Pages 284-284
    2. G. George Yin, Chao Zhu
      Pages 285-300
    3. G. George Yin, Chao Zhu
      Pages 301-321
    4. G. George Yin, Chao Zhu
      Pages 323-353
  7. Back Matter
    Pages 1-40

About this book


This book presents a comprehensive study of hybrid switching diffusion processes and their applications. The motivations for studying such processes originate from emerging and existing applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, financial engineering, and modeling, analysis, and control and optimization of large-scale systems, under the influence of random environment. One of the distinct features of the processes under consideration is the coexistence of continuous dynamics and discrete events. This book is written for applied mathematicians, applied probabilists, systems engineers, control scientists, operations researchers, and financial analysts. Selected materials from the book may also be used in a graduate level course on stochastic processes and applications or a course on hybrid systems. A large part of the book is concerned with the discrete event process depending on the continuous dynamics. In addition to the existence and uniqueness of solutions of switching diffusion equations, regularity, Feller and strong Feller properties, continuous and smooth dependence on initial data, recurrence, ergodicity, invariant measures, and stability are dealt with. Numerical methods for solutions of switching diffusions are developed; algorithms for approximation to invariant measures are investigated. Two-time-scale models are also examined. The results presented in the book are useful to researchers and practitioners who need to use stochastic models to deal with hybrid stochastic systems, and to treat real-world problems when continuous dynamics and discrete events are intertwined, in which the traditional approach using stochastic differential equations alone is no longer adequate.


Markov chain Measure continuous dynamics continuous-state-dependent switching process discrete event hybrid system recurrence stability switching diffusion

Authors and affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitU.S.A.
  2. 2.Dept. Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeU.S.A.

Bibliographic information

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From the reviews:

“The book Hybrid Switching Diffusions provides a remarkable coverage of up-to-date, cutting-edge research results on switching diffusions. … As I read through the book, I was impressed by the vast number of topics covered as well as the level of technical details. … provides a thorough, up-to-date development of regime-switching diffusions. It provides a valuable reference for applied mathematicians and control scientists. The book can also be useful to researchers in other application fields who seek suitable mathematical models that may fit their own systems.” (Ruihua Liu, IEEE Control Systems Magazine, Vol. 30, October, 2010)

“This book is written for scientists, engineers, and financial analysts interested in processes described by the coexistence of discrete events and continuous dynamics. Among the topics treated are existence and uniqueness of solutions of switching diffusion equations, regularity, well posedness, recurrence, ergodicity, stability, numerical methods, and two-time-scale processes.” (IEEE Control Systems Magazine, Vol. 30, June, 2010)