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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications

Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications

Fayolle, Guy
Iasnogorodski, Roudolf
Malyshev, Vadim

Paperback

Series: Stochastic Modelling and Applied Probability, Book 40

General MathematicsProbability & Statistics

ISBN10: 3642642179
ISBN13: 9783642642173
Publisher: Springer Nature
Published: Sep 18 2011
Pages: 156
Weight: 0.57
Height: 0.38 Width: 6.14 Depth: 9.21
Language: English
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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