Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 57-66
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Z. I. Bežaeva. Weak convergence of matrices of transition probabilities for the conditioned Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 1, pp. 57-66. http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a5/
@article{TVP_1982_27_1_a5,
author = {Z. I. Be\v{z}aeva},
title = {Weak convergence of matrices of transition probabilities for the conditioned {Markov} chains},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {57--66},
year = {1982},
volume = {27},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a5/}
}
TY - JOUR
AU - Z. I. Bežaeva
TI - Weak convergence of matrices of transition probabilities for the conditioned Markov chains
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1982
SP - 57
EP - 66
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a5/
LA - ru
ID - TVP_1982_27_1_a5
ER -
%0 Journal Article
%A Z. I. Bežaeva
%T Weak convergence of matrices of transition probabilities for the conditioned Markov chains
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1982
%P 57-66
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1982_27_1_a5/
%G ru
%F TVP_1982_27_1_a5
Let $\zeta_t=(\xi_t,\eta_t)$ be a two-dimensional countable Markov chain. The component $\xi_t\,(t=1\div n)$ may be considered as a conditioned Markov chain with respect to the conditional probability measure $\mathbf P\{\cdot\mid\eta_1,\dots,\eta_n\}$. We prove that under some assumptions all components of the matrix of transition probabilities of conditioned Markov chain converge weakly to the corresponding limits when $n\to\infty$.
