On convergence of homogeneous Markov chains

Kratochvíl, 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 -