Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 3, pp. 338-352
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I. S. Volkov. On Probabilities for Extreme Values of Sums of Random Variables Defined on a Homogeneous Markov Chain with a Finite Number of States. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 3, pp. 338-352. http://geodesic.mathdoc.fr/item/TVP_1960_5_3_a5/
@article{TVP_1960_5_3_a5,
author = {I. S. Volkov},
title = {On {Probabilities} for {Extreme} {Values} of {Sums} of {Random} {Variables} {Defined} on a {Homogeneous} {Markov} {Chain} with a {Finite} {Number} of {States}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {338--352},
year = {1960},
volume = {5},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1960_5_3_a5/}
}
TY - JOUR
AU - I. S. Volkov
TI - On Probabilities for Extreme Values of Sums of Random Variables Defined on a Homogeneous Markov Chain with a Finite Number of States
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1960
SP - 338
EP - 352
VL - 5
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1960_5_3_a5/
LA - ru
ID - TVP_1960_5_3_a5
ER -
%0 Journal Article
%A I. S. Volkov
%T On Probabilities for Extreme Values of Sums of Random Variables Defined on a Homogeneous Markov Chain with a Finite Number of States
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1960
%P 338-352
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1960_5_3_a5/
%G ru
%F TVP_1960_5_3_a5
This paper examines the probabilities for values of sums of random variables defined on a homogeneous Markov chain with a finite number of states. These values are such that their deviations from the smallest or largest possible value for each instant of time "$n$" are bounded in their sum. By separating traj ectorits in the random walk into classes defined by a proper method, regular components are picked out from the probabilities under consideration and exact and asymptotic formulas are found (for $n\to\infty$) for each of these components.
