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 - <p style="text-align: justify;">Let P be a transition matrix of a Markov chain and be of the form $$P=\Bigg( \begin{matrix} P_{11} &amp;P_{12} \\&nbsp;P_{21} &amp;P_{22}&nbsp; \end{matrix} \Bigg).$$ 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.</p>