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Probabilistic and Stochastic Methods in Analysis, with Applications

  • J. S. Byrnes
  • Jennifer L. Byrnes
  • Kathryn A. Hargreaves
  • Karl Berry

Part of the NATO ASI Series book series (ASIC, volume 372)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Wavelets and fractals

    1. Front Matter
      Pages 1-1
    2. Christopher Heil
      Pages 15-45
    3. Stéphane Mallat, Wen Liang Hwang
      Pages 47-100
    4. William Heller
      Pages 101-116
    5. John J. Benedetto
      Pages 117-161
    6. Jacques Peyrière
      Pages 175-186
    7. Gavin Brown
      Pages 207-216
    8. Bruce W. Suter, Matthew Kabrisky, Steven K. Rogers, Erik J. Fretheim, Dennis W. Ruck, Michael Mueller
      Pages 217-231
  3. Applications in engineering

  4. Applications in mathematics & computer science

  5. Stochastic calculus

    1. Front Matter
      Pages 615-615
    2. Ron C. Blei
      Pages 649-662
    3. A. Bisbas, C. Karanikas
      Pages 663-668
    4. Mauro Piccioni, Massimo Regoli
      Pages 669-685
    5. J. S. Byrnes, Jennifer L. Byrnes, Kathryn A. Hargreaves, Karl Berry
      Pages 687-690
  6. Back Matter
    Pages 691-699

About this book

Introduction

Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here.
The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

Keywords

Optimal control Stochastic calculus cognition entropy filtering filters information innovation pattern recognition wavelets

Editors and affiliations

  • J. S. Byrnes
    • 1
    • 2
  • Jennifer L. Byrnes
    • 3
  • Kathryn A. Hargreaves
    • 4
    • 1
  • Karl Berry
    • 4
    • 1
  1. 1.Prometheus Inc.NewportUSA
  2. 2.University of MassachusettsBostonUSA
  3. 3.Harvard UniversityCambridgeUSA
  4. 4.Free Software FoundationCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-2791-2
  • Copyright Information Kluwer Academic Publishers 1992
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-5239-9
  • Online ISBN 978-94-011-2791-2
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site