The spectral gap and perturbation bounds for reversible continuous-time Markov chains

被引：24

作者：

Mitrophanov, AY ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov, Russia

来源：

JOURNAL OF APPLIED PROBABILITY | 2004年 / 41卷 / 04期

关键词：

Markov chain; reversibility; eigenvalue; spectral gap; condition number; perturbation bound; sensitivity analysis;

D O I：

10.1239/jap/1101840568

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：

We show that, for reversible continuous-time Markov chains, the closeness of the nonzero eigenvalues of the generator to zero provides complete information about the sensitivity of the distribution vector to perturbations of the generator. Our results hold for both the transient and the stationary states.

引用

页码：1219 / 1222

页数：4

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