Multiparameter Processes

An Introduction to Random Fields

  • Davar Khoshnevisan

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Discrete-Parameter Random Fields

    1. Front Matter
      Pages 1-1
    2. Davar Khoshnevisan
      Pages 3-46
    3. Davar Khoshnevisan
      Pages 47-63
    4. Davar Khoshnevisan
      Pages 65-104
    5. Davar Khoshnevisan
      Pages 105-136
    6. Davar Khoshnevisan
      Pages 137-179
    7. Davar Khoshnevisan
      Pages 181-213
  3. Continuous-Parameter Random Fields

    1. Front Matter
      Pages 215-215
    2. Davar Khoshnevisan
      Pages 217-266
    3. Davar Khoshnevisan
      Pages 267-312
    4. Davar Khoshnevisan
      Pages 313-341
    5. Davar Khoshnevisan
      Pages 343-389
    6. Davar Khoshnevisan
      Pages 391-454
    7. Davar Khoshnevisan
      Pages 455-495
  4. Appendices

    1. Front Matter
      Pages 497-497
    2. Davar Khoshnevisan
      Pages 499-500
    3. Davar Khoshnevisan
      Pages 501-509
    4. Davar Khoshnevisan
      Pages 511-525
    5. Davar Khoshnevisan
      Pages 527-541

About this book

Introduction

Multiparameter processes extend the existing one-parameter theory of random processes in an elegant way, and have found connections to diverse disciplines such as probability theory, real and functional analysis, group theory, analytic number theory, and group renormalization in mathematical physics, to name a few.

This book lays the foundation of aspects of the rapidly-developing subject of random fields, and is designed for a second graduate course in probability and beyond. Its intended audience is pure, as well as applied, mathematicians.

Davar Khoshnevisan is Professor of Mathematics at the University of Utah. His research involves random fields, probabilistic potential theory, and stochastic analysis.

Keywords

Markov process Martingale Multi-parameter processes Probability Random Fields Stochastics functional analysis random walk

Authors and affiliations

  • Davar Khoshnevisan
    • 1
  1. 1.Department of MathemeticsUniversity of UtahSalt Lake CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97363
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3009-5
  • Online ISBN 978-0-387-21631-7
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book