Markov chain sensitivity measured by mean first passage times

被引：53

作者：

Cho, GE ^{[1
]}

Meyer, CD ^{[1
]}

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 316卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

Markov chains; stationary distribution; mean first passage times; stochastic matrix; sensitivity analysis; perturbation theory; stability of a Markov chain; condition numbers;

D O I：

10.1016/S0024-3795(99)00263-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to present results concerning the sensitivity of the stationary probabilities for an n-state, time-homogeneous, irreducible Markov chain in terms of the mean first passage times in the chain. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：21 / 28

页数：8

共 25 条

[1]

[Anonymous], 1979, NONNEGATIVE MATRICES

[2]

[Anonymous], RES NOTES MATH

[3]

Campbell S.L., 1991, Generalized Inverses of Linear Transformations

[4] ON THE 1ST AND 2ND ORDER DERIVATIVES OF THE PERRON VECTOR [J].

DEUTSCH, E ;

NEUMANN, M .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1985, 71 (NOV) :57-76

[5] DERIVATIVES OF THE PERRON ROOT AT AN ESSENTIALLY NONNEGATIVE MATRIX AND THE GROUP INVERSE OF AN M-MATRIX [J].

DEUTSCH, E ;

NEUMANN, M .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 102 (01) :1-29

[6] SENSITIVITY OF THE STATIONARY DISTRIBUTION VECTOR FOR AN ERGODIC MARKOV-CHAIN [J].

FUNDERLIC, RE ;

MEYER, CD .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 76 :1-17

[7] USING THE QR FACTORIZATION AND GROUP INVERSION TO COMPUTE, DIFFERENTIATE, AND ESTIMATE THE SENSITIVITY OF STATIONARY PROBABILITIES FOR MARKOV-CHAINS [J].

GOLUB, GH ;

MEYER, CD .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (02) :273-281

[8] PERTURBATION BOUNDS FOR THE STATIONARY PROBABILITIES OF A FINITE MARKOV-CHAIN [J].

HAVIV, M ;

VANDERHEYDEN, L .

ADVANCES IN APPLIED PROBABILITY, 1984, 16 (04) :804-818

[9]

Horn R. A., 1994, Matrix Analysis

[10] UNIFORM STABILITY OF MARKOV-CHAINS [J].

IPSEN, ICF ;

MEYER, CD .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1994, 15 (04) :1061-1074

← 1 2 3 →