Geodesic
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.
DOI : 10.21136/AM.1983.104012
Classification : 60J10
Keywords: convergence of distributions 
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     title = {On convergence of homogeneous {Markov} chains},
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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

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