Perturbation analysis for continuous-time Markov chains

被引:0
作者
LIU YuanYuan
机构
[1] SchoolofMathematicsandStatistics,CentralSouthUniversity
关键词
Markov chains; stationary distribution; perturbation analysis; exponential ergodicity; deviation matrix;
D O I
暂无
中图分类号
O211.62 [马尔可夫过程];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.
引用
收藏
页码:2633 / 2642
页数:10
相关论文
共 50 条
[21]   Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes [J].
Liu, Yuanyuan ;
Zhang, Yuhui .
FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (04) :933-947
[22]   Computing the Bargaining Approach for Equalizing the Ratios of Maximal Gains in Continuous-Time Markov Chains Games [J].
Trejo, Kristal K. ;
Clempner, Julio B. ;
Poznyak, Exander S. .
COMPUTATIONAL ECONOMICS, 2019, 54 (03) :933-955
[23]   A Critical Account of Perturbation Analysis of Markov Chains [J].
Abbas, K. ;
Berkhout, J. ;
Heidergott, B. .
MARKOV PROCESSES AND RELATED FIELDS, 2016, 22 (02) :227-265
[24]   Blockwise perturbation theory for Markov chains [J].
Xue, JG ;
Gao, WG .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1998, 20 (01) :270-278
[25]   Estimation-Calibration of Continuous-Time Non-Homogeneous Markov Chains with Finite State Space [J].
Esquivel, Manuel L. ;
Krasii, Nadezhda P. ;
Guerreiro, Gracinda R. .
MATHEMATICS, 2024, 12 (05)
[26]   PERTURBATION BOUNDS FOR THE STATIONARY DISTRIBUTIONS OF MARKOV CHAINS [J].
Liu, Yuanyuan .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2012, 33 (04) :1057-1074
[27]   SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS [J].
Thiede, Erik ;
Van Koten, Brian ;
Weare, Jonathan .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (03) :917-941
[28]   IMPROVED PERTURBATION BOUNDS FOR THE CONTINUOUS-TIME H∞-CONTROL PROBLEM [J].
Christov, Nicolai D. ;
Konstantinov, Mihail M. ;
Petkov, Petko Hr. .
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2014, 43 :90-99
[29]   Modeling Emergency Traffic Using a Continuous-Time Markov Chain [J].
El Fawal, Ahmad Hani ;
Mansour, Ali ;
El Ghor, Hussein ;
Ismail, Nuha A. ;
Shamaa, Sally .
JOURNAL OF SENSOR AND ACTUATOR NETWORKS, 2024, 13 (06)
[30]   Perturbation analysis for denumerable Markov chains with application to queueing models [J].
Altman, E ;
Avrachenkov, KE ;
Núñez-Queija, R .
ADVANCES IN APPLIED PROBABILITY, 2004, 36 (03) :839-853