Skip to main content
SpringerLink
Log in
Book cover

Multiparameter Processes

An Introduction to Random Fields

  • Book
  • © 2002

Overview

Authors:
  1. Davar Khoshnevisan

    1. Department of Mathemetics, University of Utah, Salt Lake City, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Discrete-Parameter Random Fields

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Discrete-Parameter Martingales

      • Davar Khoshnevisan
      Pages 3-46

    3. Two Applications in Analysis

      • Davar Khoshnevisan
      Pages 47-63

    4. Random Walks

      • Davar Khoshnevisan
      Pages 65-104

    5. Multiparameter Walks

      • Davar Khoshnevisan
      Pages 105-136

    6. Gaussian Random Variables

      • Davar Khoshnevisan
      Pages 137-179

    7. Limit Theorems

      • Davar Khoshnevisan
      Pages 181-213

  3. Continuous-Parameter Random Fields

    1. Front Matter

      Pages 215-215
      Download chapter PDF

    2. Continuous-Parameter Martingales

      • Davar Khoshnevisan
      Pages 217-266

    3. Constructing Markov Processes

      • Davar Khoshnevisan
      Pages 267-312

    4. Generation of Markov Processes

      • Davar Khoshnevisan
      Pages 313-341

    5. Probabilistic Potential Theory

      • Davar Khoshnevisan
      Pages 343-389

    6. Multiparameter Markov Processes

      • Davar Khoshnevisan
      Pages 391-454

    7. The Brownian Sheet and Potential Theory

      • Davar Khoshnevisan
      Pages 455-495

  4. Appendices

    1. Front Matter

      Pages 497-497
      Download chapter PDF

    2. Kolmogorov’s Consistency Theorem

      • Davar Khoshnevisan
      Pages 499-500

    3. Laplace Transforms

      • Davar Khoshnevisan
      Pages 501-509

    4. Hausdorff Dimensions and Measures

      • Davar Khoshnevisan
      Pages 511-525

    5. Energy and Capacity

      • Davar Khoshnevisan
      Pages 527-541
Back to top

Keywords

About this book

Multi-parameter processes extend the existing one-parameter theory in an elegant way and have many applications to other fields in mathematics such as real analysis, functional analysis, group theory, and analytic number theory, to name a few. This book on the vast and rapidly developing subject of random fields is designed for a second graduate course in probability. Recent work on random fields has made it possible to make it an expository subject which interacts with several other areas in mathematics and has enough mathematical depth to be of use to pure as well as applied mathematicians of many backgrounds.

Reviews

From the reviews:

"This book presents an updated and comprehensible account on the theory of multiparameter stochastic processes. … This book is certainly a basic reference for subjects like multiparameter martingales and potential theory for the Brownian sheet and several Markov processes. It can be useful for researchers who would like to learn the basis and recent developments of these subjects. The book is self-contained … . In spite of the technical character of the subject, reading this book is a very pleasant and enriching experience." (David Nualart, Mathematical Reviews, Issue 2004 a)

"This book aims to construct a general framework for the analysis of a large class of random fields, also known as multiparameter processes. A great part of one-parameter theory is also included, with the goal to keep the book self-contained. … The book contains a lot of supplementary exercises, extended theoretical appendices and is useful both for highly qualified specialists and for advanced graduate students." (Yu. S. Mishura, Zentralblatt Math, Vol. 1005, 2003)

"The present book is the first one presenting a general treatment of random fields. … The book can be recommended not only to probabilists but to anyone interested in the applications of probability within other areas of mathematics, particularly in analysis." (P. Révész, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003)

Authors and Affiliations

  • Department of Mathemetics, University of Utah, Salt Lake City, USA

    Davar Khoshnevisan

Bibliographic Information

  • Book Title: Multiparameter Processes

  • Book Subtitle: An Introduction to Random Fields

  • Authors: Davar Khoshnevisan

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/b97363

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 2002

  • Hardcover ISBN: 978-0-387-95459-2Published: 10 July 2002

  • Softcover ISBN: 978-1-4419-3009-5Published: 11 August 2011

  • eBook ISBN: 978-0-387-21631-7Published: 10 April 2006

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XX, 584

  • Number of Illustrations: 8 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes, Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation