Random Walks in the Quarter Plane by Guy Fayolle Roudolf Iasnogorodski & Vadim Malyshev

Author:Guy Fayolle, Roudolf Iasnogorodski & Vadim Malyshev
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.2.6)

where , the space of continuous functions on , and . A priori g and G are only defined on .

For our purpose, we shall only consider the problem for G, and also assume that G does not vanish on .

Notation We introduce the following important quantity

(5.2.7)

which will be called the index and represents the variation of the argument of G(t), as t moves along the contour in the positive direction.

Without loss of generality, we shall suppose that the origin of the coordinate system lies in the domain . Then the function

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