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商品コード: 9783319509280

Random Walks in the Quarter Plane

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分野別 > 数学 > 統計学・確率論

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書名

Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
著者・編者 Fayolle, G. et al.
出版社/発行元 Springer
発行年/月 2017年2月   
装丁 Hardcover
ページ数/巻数 248 ページ
ISBN 978-3-319-50928-0
発送予定 海外倉庫よりお取り寄せ 2-3週間以内に発送します

 

Desciption

 

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts.


Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems.

Part II borrows special case-studies from queueing theory (in particular, the famous problem of Joining the Shorter of Two Queues) and enumerative combinatorics (Counting, Asymptotics).

Researchers and graduate students should find this book very useful.

 

Contents:

 

Part I The General Theory
1 Probabilistic Background
2 Foundations of the Analytic Approach
3 Analytic Continuation of the Unknown Functions in the Genus 1 Case
4 The Case of a Finite Group
5 Solution in the Case of an Arbitrary Group
6 The Genus 0 Case
7 Criterion for the Finiteness of the Group in the Genus 0 Case
8 Miscellanea

Part II Applications to Queueing Systems and Analytic Combinatorics
9 A Two-Coupled Processor Model
10 Joining the Shorter of Two Queues: Reduction to a Generalized BVP
11 Counting Lattice Walks in the Quarter Plane

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