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Random Perturbation Methods with Applications in Science and Engineering

  • Anatoli V. Skorokhod
  • Frank C. Hoppensteadt
  • Habib Salehi

Part of the Applied Mathematical Sciences book series (AMS, volume 150)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 1-48
  3. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 49-63
  4. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 64-87
  5. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 88-113
  6. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 114-132
  7. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 133-171
  8. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 172-231
  9. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 232-256
  10. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 257-302
  11. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 303-342
  12. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 343-375
  13. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 376-423
  14. Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi
    Pages 424-451
  15. Back Matter
    Pages 452-490

About this book

Introduction

As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations.
This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems.

Keywords

Dynamical systems Markov Pertubation Probability theory Random dynamical systems Random pertubation Random pertubation method Simulation Stochastic processes dynamische Systeme

Authors and affiliations

  • Anatoli V. Skorokhod
    • 1
    • 2
  • Frank C. Hoppensteadt
    • 3
  • Habib Salehi
    • 4
  1. 1.Institute of MathematicsUkrainian Academy of ScienceKievUkraine
  2. 2.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA
  3. 3.Systems Science and Engineering Research CenterArizona State UniversityTempeUSA
  4. 4.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b98905
  • Copyright Information Springer Science+Business Media New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9271-2
  • Online ISBN 978-0-387-22446-6
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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