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Random Walks in the Quarter-Plane

Algebraic Methods, Boundary Value Problems and Applications

  • Guy Fayolle
  • Roudolf Iasnogorodski
  • Vadim Malyshev

Table of contents

  1. Front Matter
    Pages I-XV
  2. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 1-6
  3. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 7-33
  4. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 35-49
  5. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 51-91
  6. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 93-127
  7. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 129-143
  8. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 145-150
  9. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages E1-E4
  10. Back Matter
    Pages 151-154

About this book

Introduction

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.

Keywords

Markov chain Riemann surfaces functional equations measure queuing theory random walk random walks uniformization

Authors and affiliations

  • Guy Fayolle
    • 1
  • Roudolf Iasnogorodski
    • 2
  • Vadim Malyshev
    • 1
  1. 1.Domaine de Voluceau, RocquencourtINRIALe ChesnayFrance
  2. 2.Department of MathematicsUniversity of OrléansOrléans la SourceFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-60001-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64217-3
  • Online ISBN 978-3-642-60001-2
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site
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