Schwarz methods for quasi stationary distributions of Markov chains

被引:0
作者
Guangbao Guo
Weidong Zhao
机构
[1] Shandong University,School of Mathematics
来源
Calcolo | 2012年 / 49卷
关键词
Schwarz methods; Markov chains; Quasi stationary distributions; Quasi nonnegative splittings; 60J22; 60J10; 65C40; 65F10;
D O I
暂无
中图分类号
学科分类号
摘要
We study computational schemes for quasi stationary distributions of Markov chains, having matrices which are quasi stochastic, i.e., all of their row sums are less than or equal to one. We develop Schwarz methods for the corresponding distributions. In particular, we get the semiconvergence of additive and multiplicative Schwarz methods, and that of two level Schwarz iterative methods for the quasi stationary distributions (QSDs). We provide two examples of Markov chains with QSDs, to explain our methods.
引用
收藏
页码:21 / 39
页数:18
相关论文
共 50 条
[41]   QUASI-STATIONARY DISTRIBUTIONS AND DIFFUSION MODELS IN POPULATION DYNAMICS [J].
Cattiaux, Patrick ;
Collet, Pierre ;
Lambert, Amaury ;
Martinez, Servet ;
Meleard, Sylvie ;
San Martin, Jaime .
ANNALS OF PROBABILITY, 2009, 37 (05) :1926-1969
[42]   Quasi-stationary and ratio of expectations distributions: A comparative study [J].
Artalejo, J. R. ;
Lopez-Herrero, M. J. .
JOURNAL OF THEORETICAL BIOLOGY, 2010, 266 (02) :264-274
[43]   Parisian quasi-stationary distributions for asymmetric Levy processes [J].
Czarna, Irmina ;
Palmowski, Zbigniew .
STATISTICS & PROBABILITY LETTERS, 2017, 127 :75-84
[44]   Analysis of distributed systems via quasi-stationary distributions [J].
Champagnat, Nicolas ;
Schott, Rene ;
Villemonais, Denis .
STOCHASTIC ANALYSIS AND APPLICATIONS, 2021, 39 (06) :981-998
[45]   Quasi-optimal Schwarz methods for the conforming spectral element discretization [J].
Casarin, MA .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (06) :2482-2502
[46]   PHASE-TYPE DISTRIBUTIONS AND THE STRUCTURE OF FINITE MARKOV-CHAINS [J].
MAIER, RS .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1993, 46 (03) :449-453
[47]   The asymptotic tails of limit distributions of continuous-time Markov chains [J].
Xu, Chuang ;
Hansen, Mads Christian ;
Wiuf, Carsten .
ADVANCES IN APPLIED PROBABILITY, 2024, 56 (02) :693-734
[48]   CHARACTERIZATION OF THE CONDITIONAL STATIONARY DISTRIBUTION IN MARKOV CHAINS VIA SYSTEMS OF LINEAR INEQUALITIES [J].
Kimura, Masatoshi ;
Takine, Tetsuya .
ADVANCES IN APPLIED PROBABILITY, 2020, 52 (04) :1249-1283
[49]   Computing closed-form stochastic bounds on the stationary distribution of Markov chains [J].
Ben Mamoun, M ;
Pekergin, N .
MATHEMATICS AND COMPUTER SCIENCE: ALGORITHMS, TREES, COMBINATORICS AND PROBABILITIES, 2000, :197-208
[50]   Domain of attraction of quasi-stationary distributions for the Brownian motion with drift [J].
Martinez, S ;
Picco, P ;
San Martin, J .
ADVANCES IN APPLIED PROBABILITY, 1998, 30 (02) :385-408