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Stochastic Modelling and Applied Probability

Random Walks in the Quarter-Plane

Algebraic Methods, Boundary Value Problems and Applications

Authors: Fayolle, Guy, Iasnogorodski, Roudolf, Malyshev, Vadim

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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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-642-60001-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-642-64217-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Random Walks in the Quarter-Plane
Book Subtitle
Algebraic Methods, Boundary Value Problems and Applications
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
40
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-60001-2
DOI
10.1007/978-3-642-60001-2
Softcover ISBN
978-3-642-64217-3
Series ISSN
0172-4568
Edition Number
1
Number of Pages
XV, 156
Topics

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