Details

Autor(en) / Beteiligte

• Fayolle, Guy
• Iasnogorodski, Roudolf
• Malyshev, Vadim

Titel

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

Ist Teil von

• Applications of Mathematics Stochastic Modelling and Applied Probability : 40

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1999

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• Historical Comments Two-dimensional random walks in domains with non-smooth boundaries interest several groups of the mathematical community. In fact these objects are encountered in pure probabilistic problems, as well as in applications involving 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