QUASI-BIRTH-AND-DEATH PROCESSES, LATTICE PATH COUNTING, AND HYPERGEOMETRIC FUNCTIONS

被引：17

作者：

Van Leeuwaarden, Johan S. H. ^{[1
]}

Squillante, Mark S. ^{[3
]}

Winands, Erik M. M. ^{[2
,4
]}

机构：

[1] EURANDOM, NL-5600 MB Eindhoven, Netherlands

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[3] IBM Corp, Thomas J Watson Res Ctr, Dept Math Sci, Yorktown Hts, NY 10598 USA

[4] Eindhoven Univ Technol, Dept Technol Management, NL-5600 MB Eindhoven, Netherlands

来源：

JOURNAL OF APPLIED PROBABILITY | 2009年 / 46卷 / 02期

关键词：

Quasi-birth-and-death process; matrix-analytic methods; rate matrix; lattice path counting; hypergeometric function;

D O I：

10.1239/jap/1245676103

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we consider a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G. The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.

引用

页码：507 / 520

页数：14

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