Titlebook: Random Walks in the Quarter-Plane; Algebraic Methods, B Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev Book 19991st edition Springer-Verl

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Book 19991st editionkhotski, 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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The Case of a Finite Group,functions .,.,.. are polynomials. In this case, we are able to characterize completely the solutions of the basic functional equation, and also to give necessary and sufficient conditions for these solutions to be rational or algebraic.

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Solution in the Case of an Arbitrary Group,e group. Hereafter, we shall obtain the complete solution when the order of the group of the random walk is arbitrary, i.e. possibly infinite. The main idea consists in the reduction to a factorization problem on a curve in the complex plane. Generally one comes up first with integral equations and,

BARB

The Genus 0 Case, in Chapter 2 and exactly five situations have been found, described by the relations (2.3.5) to (2.3.8). In fact, since (2.3.6) and (2.3.8) are equivalent up to a permutation of the variables . and ., we are left with four significantly different cases, which will be treated separately.

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