This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behaviour of random walks in the quarter-plane.Algebraic Methods, Boundary Value Problems and Applications Guy Fayolle, Roudolf Iasnogorodski, Vadim Aleksandrovich Malyshev ... Then equation (4-S.5) has a rational solution if, and only if, n-l n-l n ^=Ad- k=0 i=k+l Moreover, under this condition, the solution is ... Setting w = en, (4.2.5) finally reduces to ws-w = csiagt;.
|Title||:||Random Walks in the Quarter-Plane|
|Author||:||Guy Fayolle, Roudolf Iasnogorodski, Vadim Aleksandrovich Malyshev|
|Publisher||:||Springer Science & Business Media - 1999-05-04|