Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 789-794
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Yu. P. Filonov. Expectations of the moments of reaching the level by the range type functionals for Markov chain. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 789-794. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a18/
@article{TVP_1983_28_4_a18,
author = {Yu. P. Filonov},
title = {Expectations of the moments of reaching the level by the range type functionals for {Markov} chain},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {789--794},
year = {1983},
volume = {28},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a18/}
}
TY - JOUR
AU - Yu. P. Filonov
TI - Expectations of the moments of reaching the level by the range type functionals for Markov chain
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1983
SP - 789
EP - 794
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a18/
LA - ru
ID - TVP_1983_28_4_a18
ER -
%0 Journal Article
%A Yu. P. Filonov
%T Expectations of the moments of reaching the level by the range type functionals for Markov chain
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 789-794
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a18/
%G ru
%F TVP_1983_28_4_a18
Let $S_0,S_1,\dots$ be a homogeneous Markov chain on the set of integers, $$ \tau_N=\min\{n:\sup_{0\le i,j\le n}(S_i-S_j)\ge N\},\qquad\bar\tau_n=\min\{n:\operatorname{card}\{S_0,\dots,S_n\}=N\}. $$ Theorems on the asymptotical behaviour of $\mathbf M\tau_n$ and $\mathbf M\bar\tau_n$ are proved.
