Volume 18, Issue 3
Blockwise Perturbation Theory for 2x2 Block Markov Chains
DOI:

J. Comp. Math., 18 (2000), pp. 305-312

Published online: 2000-06

Preview Full PDF 93 1667
Export citation

Cited by

• Abstract

Let P be a transition matrix of a Markov chain and be of the form $$P = \left( \begin{array}{cc}P_{11} & P_{22} \\ P_{21} & P_{22} \right).$$ The stationary distribution $\pi^T$ is partitioned conformally in the form (\pi^T_1, \pi^T_2). This paper establish the relative error bound in $\pi^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation.

• Keywords

Blockwise perturbation Markov chains stationary distribution error bound

@Article{JCM-18-305, author = {}, title = {Blockwise Perturbation Theory for 2x2 Block Markov Chains}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {3}, pages = {305--312}, abstract = { Let P be a transition matrix of a Markov chain and be of the form $$P = \left( \begin{array}{cc}P_{11} & P_{22} \\ P_{21} & P_{22} \right).$$ The stationary distribution $\pi^T$ is partitioned conformally in the form (\pi^T_1, \pi^T_2). This paper establish the relative error bound in $\pi^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9044.html} }
TY - JOUR T1 - Blockwise Perturbation Theory for 2x2 Block Markov Chains JO - Journal of Computational Mathematics VL - 3 SP - 305 EP - 312 PY - 2000 DA - 2000/06 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9044.html KW - Blockwise perturbation KW - Markov chains KW - stationary distribution KW - error bound AB - Let P be a transition matrix of a Markov chain and be of the form $$P = \left( \begin{array}{cc}P_{11} & P_{22} \\ P_{21} & P_{22} \right).$$ The stationary distribution $\pi^T$ is partitioned conformally in the form (\pi^T_1, \pi^T_2). This paper establish the relative error bound in $\pi^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation.