Digraph-based conditioning for Markov chains

被引：4

作者：

Kirkland, S ^{[1
]}

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 385卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

stochastic matrix; Markov chain; stationary vectors; condition number; directed graph;

D O I：

10.1016/S0024-3795(03)00495-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an irreducible stochastic matrix T, we consider a certain condition number c(T), which measures the stability of the corresponding stationary distribution when T is perturbed. We characterize the strongly connected directed graphs D such that c(T) is bounded as T ranges over T-D, the set of stochastic matrices whose directed graph is contained in D. For those digraphs D for which c(T) is bounded, we find the maximum value of c(T) as T ranges over T-D. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：81 / 93

页数：13

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