Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability, 40) - Hardcover

Fayolle, Guy; Iasnogorodski, Roudolf; Malyshev, Vadim

Hardcover

ISBN 10: 3540650474 ISBN 13: 9783540650478

Verlag: Springer, 1999

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1999
• Sprache: Englisch
• ISBN 10: 3540650474
• ISBN 13: 9783540650478
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 171
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland