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  • Book
  • © 1999

Random Walks in the Quarter-Plane

Algebraic Methods, Boundary Value Problems and Applications

Authors:

  1. Guy Fayolle

    1. Domaine de Voluceau, Rocquencourt, INRIA, Le Chesnay, France

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  2. Roudolf Iasnogorodski

    1. Department of Mathematics, University of Orléans, Orléans la Source, France

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  3. Vadim Malyshev

    1. Domaine de Voluceau, Rocquencourt, INRIA, Le Chesnay, France

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Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 40)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XV
    PDF

  2. Probabilistic Background

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 1-6

  3. Foundations of the Analytic Approach

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 7-33

  4. Analytic Continuation of the Unknown Functions in the Genus 1 Case

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 35-49

  5. The Case of a Finite Group

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 51-91

  6. Solution in the Case of an Arbitrary Group

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 93-127

  7. The Genus 0 Case

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 129-143

  8. Miscellanea

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 145-150

  9. Erratum

    • Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages E1-E4

  10. Back Matter

    Pages 151-154
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About this book

Historical Comments Two-dimensional random walks in domains with non-smooth boundaries inter­ est several groups of the mathematical community. In fact these objects are encountered in pure probabilistic problems, as well as in applications involv­ ing queueing theory. This monograph aims at promoting original mathematical methods to determine the invariant measure of such processes. Moreover, as it will emerge later, these methods can also be employed to characterize the transient behavior. It is worth to place our work in its historical context. This book has three sources. l. Boundary value problems for functions of one complex variable; 2. Singular integral equations, Wiener-Hopf equations, Toeplitz operators; 3. Random walks on a half-line and related queueing problems. The first two topics were for a long time in the center of interest of many well known mathematicians: Riemann, Sokhotski, Hilbert, Plemelj, Carleman, Wiener, Hopf. This one-dimensional theory took its final form in the works of Krein, Muskhelishvili, Gakhov, Gokhberg, etc. The third point, and the related probabilistic problems, have been thoroughly investigated by Spitzer, Feller, Baxter, Borovkov, Cohen, etc.
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Keywords

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Authors and Affiliations

  • Domaine de Voluceau, Rocquencourt, INRIA, Le Chesnay, France

    Guy Fayolle, Vadim Malyshev

  • Department of Mathematics, University of Orléans, Orléans la Source, France

    Roudolf Iasnogorodski

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Bibliographic Information

  • Book Title: Random Walks in the Quarter-Plane

  • Book Subtitle: Algebraic Methods, Boundary Value Problems and Applications

  • Authors: Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

  • Series Title: Stochastic Modelling and Applied Probability

  • DOI: https://doi.org/10.1007/978-3-642-60001-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-642-64217-3Published: 18 September 2011

  • eBook ISBN: 978-3-642-60001-2Published: 06 December 2012

  • Series ISSN: 0172-4568

  • Series E-ISSN: 2197-439X

  • Edition Number: 1

  • Number of Pages: XV, 156

  • Topics: Probability Theory and Stochastic Processes, Analysis, Statistical Theory and Methods

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Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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