On convergence of homogeneous Markov chains
Applications of Mathematics, Tome 28 (1983) no. 2, pp. 116-119
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Let $p_t$ be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences $\left\|p_{t+2}-p_{t+1}\right\|\left\|p_{t+1}-p_t\right\|$. In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.
Let $p_t$ be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences $\left\|p_{t+2}-p_{t+1}\right\|\left\|p_{t+1}-p_t\right\|$. In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.
Kratochvíl, Petr. On convergence of homogeneous Markov chains. Applications of Mathematics, Tome 28 (1983) no. 2, pp. 116-119. doi: 10.21136/AM.1983.104012
@article{10_21136_AM_1983_104012,
author = {Kratochv{\'\i}l, Petr},
title = {On convergence of homogeneous {Markov} chains},
journal = {Applications of Mathematics},
pages = {116--119},
year = {1983},
volume = {28},
number = {2},
doi = {10.21136/AM.1983.104012},
mrnumber = {0695185},
zbl = {0511.60065},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104012/}
}
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