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

Jun-Gong Xue & Wei-Guo Gao

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

Published online: 2000-06

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  • Abstract

Let P be a transition matrix of a Markov chain and be of the form $$P=\Bigg( \begin{matrix} P_{11} &P_{12} \\ P_{21} &P_{22}  \end{matrix} \Bigg).$$ The stationary distribution $π^T$ is partitioned conformally in the form $(π^T_1, π^T_2)$. This paper establish the relative error bound in $π^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation.

  • Keywords

Blockwise perturbation, Markov chains, stationary distribution, error bound.

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COPYRIGHT: © Global Science Press

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@Article{JCM-18-305, author = {Xue , Jun-Gong and Gao , Wei-Guo}, 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 $$P=\Bigg( \begin{matrix} P_{11} &P_{12} \\ P_{21} &P_{22}  \end{matrix} \Bigg).$$ The stationary distribution $π^T$ is partitioned conformally in the form $(π^T_1, π^T_2)$. This paper establish the relative error bound in $π^T_i (i=1,2)$ 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 AU - Xue , Jun-Gong AU - Gao , Wei-Guo 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, Markov chains, stationary distribution, error bound. AB -

Let P be a transition matrix of a Markov chain and be of the form $$P=\Bigg( \begin{matrix} P_{11} &P_{12} \\ P_{21} &P_{22}  \end{matrix} \Bigg).$$ The stationary distribution $π^T$ is partitioned conformally in the form $(π^T_1, π^T_2)$. This paper establish the relative error bound in $π^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation.

Jun-Gong Xue & Wei-Guo Gao. (1970). Blockwise Perturbation Theory for 2x2 Block Markov Chains. Journal of Computational Mathematics. 18 (3). 305-312. doi:
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