# On convergence of homogeneous Markov chains

Aplikace matematiky (1983)

- Volume: 28, Issue: 2, page 116-119
- ISSN: 0862-7940

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topKratochvíl, Petr. "On convergence of homogeneous Markov chains." Aplikace matematiky 28.2 (1983): 116-119. <http://eudml.org/doc/15283>.

@article{Kratochvíl1983,

abstract = {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\Vert p_\{t+2\}-p_\{t+1\}\right\Vert <\left\Vert p_\{t+1\}-p_t\right\Vert $. 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.},

author = {Kratochvíl, Petr},

journal = {Aplikace matematiky},

keywords = {convergence of distributions},

language = {eng},

number = {2},

pages = {116-119},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On convergence of homogeneous Markov chains},

url = {http://eudml.org/doc/15283},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Kratochvíl, Petr

TI - On convergence of homogeneous Markov chains

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 2

SP - 116

EP - 119

AB - 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\Vert p_{t+2}-p_{t+1}\right\Vert <\left\Vert p_{t+1}-p_t\right\Vert $. 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.

LA - eng

KW - convergence of distributions

UR - http://eudml.org/doc/15283

ER -

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