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Hybrid Switching Diffusions

Properties and Applications

  • Book
  • © 2010

Overview

Authors:
  1. G. George Yin

    1. Department of Mathematics, Wayne State University, Detroit, U.S.A.

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    You can also search for this author in PubMed   Google Scholar

  2. Chao Zhu

    1. Dept. Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, U.S.A.

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Chapter summaries
  • Detailed Illustrations
  • Many worked out examples
  • Numerical Solutions
  • Applications to Finance
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages 1-15
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  2. Introduction and Motivation

    • G. George Yin, Chao Zhu
    Pages 1-24

  3. Basic Properties, Recurrence, Ergodicity

    1. Front Matter

      Pages 26-26
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    2. Switching Diffusion

      • G. George Yin, Chao Zhu
      Pages 27-67

    3. Recurrence

      • G. George Yin, Chao Zhu
      Pages 69-109

    4. Ergodicity

      • G. George Yin, Chao Zhu
      Pages 111-134

  4. Numerical Solutions and Approximation

    1. Front Matter

      Pages 136-136
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    2. Numerical Approximation

      • G. George Yin, Chao Zhu
      Pages 137-157

    3. Numerical Approximation to Invariant Measures

      • G. George Yin, Chao Zhu
      Pages 159-179

  5. Stability

    1. Front Matter

      Pages 182-182
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    2. Stability

      • G. George Yin, Chao Zhu
      Pages 183-215

    3. Stability of Switching ODEs

      • G. George Yin, Chao Zhu
      Pages 217-250

    4. Invariance Principles

      • G. George Yin, Chao Zhu
      Pages 251-281

  6. Two-Time-Scale Modeling and Applications

    1. Front Matter

      Pages 284-284
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  7. Two-time-scale Modeling and Applications

    1. Positive Recurrence: Weakly Connected Ergodic Classes

      • G. George Yin, Chao Zhu
      Pages 285-300

    2. Stochastic Volatility Using Regime-Switching Diffusions

      • G. George Yin, Chao Zhu
      Pages 301-321

    3. Two-Time-Scale Switching Jump Diffusions

      • G. George Yin, Chao Zhu
      Pages 323-353

  8. Back Matter

    Pages 1-40
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Keywords

About this book

This book encompasses the study of hybrid switching di usion processes and their applications. The word \hybrid" signi es the coexistence of c- tinuous dynamics and discrete events, which is one of the distinct features of the processes under consideration. Much of the book is concerned with the interactions of the continuous dynamics and the discrete events. Our motivations for studying such processes originate from emerging and - isting applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, nancial engineering, and modeling, analysis, and control and optimization of lar- scale systems, under the in uence of random environments. Displaying mixture distributions, switching di usions may be described by the associated operators or by systems of stochastic di erential eq- tions together with the probability transition laws of the switching actions. We either have Markov-modulated switching di usions or processes with continuous state-dependent switching. The latter turns out to be much more challenging to deal with. Viewing the hybrid di usions as a number of di usions joined together by the switching process, they may be se- ingly not much di erent from their di usion counterpart. Nevertheless, the underlying problems become more di cult to handle, especially when the switching processes depend on continuous states. The di culty is due to the interaction of the discrete and continuous processes and the tangled and hybrid information pattern.

Reviews

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)

Authors and Affiliations

  • Department of Mathematics, Wayne State University, Detroit, U.S.A.

    G. George Yin

  • Dept. Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, U.S.A.

    Chao Zhu

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