Adaptive Algorithms and Stochastic Approximations

  • Albert Benveniste
  • Michel Métivier
  • Pierre Priouret

Part of the Applications of Mathematics book series (SMAP, volume 22)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction

    1. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 1-6
  3. Adaptive Algorithms: Applications

    1. Front Matter
      Pages 7-7
    2. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 9-39
    3. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 40-102
    4. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 103-119
    5. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 120-164
    6. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 165-198
    7. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 199-210
  4. Stochastic Approximations: Theory

    1. Front Matter
      Pages 211-211
    2. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 213-250
    3. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 251-288
    4. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 289-306
    5. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 307-342
    6. Albert Benveniste, Michel Métivier, Pierre Priouret
      Pages 343-347
  5. Back Matter
    Pages 349-365

About this book

Introduction

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "intelligence" within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a "general theory of adaptive systems" encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.

Keywords

Extension Markov chain Moment Parameter Rang System identification behavior cognition control ergodicity intelligence modeling pattern recognition statistics stochastic approximation

Authors and affiliations

  • Albert Benveniste
    • 1
  • Michel Métivier
  • Pierre Priouret
    • 2
  1. 1.IRISA-INRIARennes CedexFrance
  2. 2.Laboratoire de ProbabilitésUniversité Pierre et Marie CurieParis CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-75894-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-75896-6
  • Online ISBN 978-3-642-75894-2
  • Series Print ISSN 0172-4568
  • About this book