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Blockwise Perturbation Theory for 2x2 Block Markov Chains
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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.
Xue , Jun-Gong and Gao , Wei-Guo. (2000). Blockwise Perturbation Theory for 2x2 Block Markov Chains.
Journal of Computational Mathematics. 18 (3).
305-312.
doi:
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