Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
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DOI：
10.1007/978-3-319-50930-3
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
G. Fayolle;R. Iasnogorodski;V. Malyshev
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文献类型：
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作者：
G. Fayolle;R. Iasnogorodski;V. Malyshev
近几十年来，非光滑边界域中的二维随机游走变得越来越流行，并且引起了数学界多个团体的兴趣。事实上，这些马尔可夫对象在纯概率问题以及涉及排队论和最近的枚举组合学的应用中都会遇到。本专着是第一版（1999）的延续，旨在推广原始数学方法来确定此类过程的不变测度。此外，这些方法也可用于表征瞬态行为。复变函数理论、边值问题、黎曼曲面、函数方程和伽罗瓦理论是我们的目的所需的主要数学成分。
In recent decades, two-dimensional random walks in domains with non-smooth boundaries became increasingly popular and are of interest to several groups in the mathematical community. In fact, these Markovian objects are encountered in pure probabilistic problems, as well as in applications involving queueing theory and, more recently, enumerative combinatorics. This monograph is the continuation of the first edition (1999), aiming to promote original mathematical methods to determine the invariant measure of such processes. Moreover, these methods can also be employed to characterize the transient behavior. Complex function theory, boundary value problems, Riemann surfaces, functional equations, and Galois theory are the main mathematical ingredients necessary for our purpose.