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Two-Scale Stochastic Systems

Asymptotic Analysis and Control

  • Yuri Kabanov
  • Sergei Pergamenshchikov

Part of the Applications of Mathematics book series (SMAP, volume 49)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 1-17
  3. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 19-41
  4. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 43-85
  5. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 87-109
  6. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 111-144
  7. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 145-192
  8. Yuri Kabanov, Sergei Pergamenshchikov
    Pages 193-222
  9. Back Matter
    Pages 223-266

About this book

Introduction

Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Keywords

Approximation Stochastic differential equations optimal control singular perturbations stochastic approximation stochastic control system two-scale stochastic systems

Authors and affiliations

  • Yuri Kabanov
    • 1
  • Sergei Pergamenshchikov
    • 2
  1. 1.Département de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance
  2. 2.LIFAR, UFR Sciences et TechniquesUniversité de RouenMont Saint Aignan CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-13242-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08467-6
  • Online ISBN 978-3-662-13242-5
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site