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
收藏
页码：1219 / 1222
页数：4
相关论文
共 50 条
  • [21] Generalization Bounds of ERM-Based Learning Processes for Continuous-Time Markov Chains
    Zhang, Chao
    Tao, Dacheng
    IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2012, 23 (12) : 1872 - 1883
  • [22] Ergodic degrees for continuous-time Markov chains
    Mao, YH
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2004, 47 (02): : 161 - 174
  • [23] Ergodic degrees for continuous-time Markov chains
    MAO YonghuaDepartment of Mathematics
    Science China Mathematics, 2004, (02) : 161 - 174
  • [24] Interval Continuous-Time Markov Chains Simulation
    Galdino, Sergio
    2013 INTERNATIONAL CONFERENCE ON FUZZY THEORY AND ITS APPLICATIONS (IFUZZY 2013), 2013, : 273 - 278
  • [25] On Nonergodicity of Some Continuous-Time Markov Chains
    D. B. Andreev
    E. A. Krylov
    A. I. Zeifman
    Journal of Mathematical Sciences, 2004, 122 (4) : 3332 - 3335
  • [26] Lumpability for Uncertain Continuous-Time Markov Chains
    Cardelli, Luca
    Grosu, Radu
    Larsen, Kim G.
    Tribastone, Mirco
    Tschaikowski, Max
    Vandin, Andrea
    QUANTITATIVE EVALUATION OF SYSTEMS (QEST 2021), 2021, 12846 : 391 - 409
  • [27] SIMILAR STATES IN CONTINUOUS-TIME MARKOV CHAINS
    Yap, V. B.
    JOURNAL OF APPLIED PROBABILITY, 2009, 46 (02) : 497 - 506
  • [28] Matrix Analysis for Continuous-Time Markov Chains
    Le, Hung, V
    Tsatsomeros, M. J.
    SPECIAL MATRICES, 2021, 10 (01): : 219 - 233
  • [29] Algorithmic Randomness in Continuous-Time Markov Chains
    Huang, Xiang
    Lutz, Jack H.
    Migunov, Andrei N.
    2019 57TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON), 2019, : 615 - 622
  • [30] Path integrals for continuous-time Markov chains
    Pollett, PK
    Stefanov, VT
    JOURNAL OF APPLIED PROBABILITY, 2002, 39 (04) : 901 - 904
12345