Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 873-879
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V. I. Lotov. Asymptotic analysis of distributions in the problems with two boundaries. II. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 4, pp. 873-879. http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a20/
@article{TVP_1979_24_4_a20,
author = {V. I. Lotov},
title = {Asymptotic analysis of distributions in the problems with two {boundaries.~II}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {873--879},
year = {1979},
volume = {24},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a20/}
}
TY - JOUR
AU - V. I. Lotov
TI - Asymptotic analysis of distributions in the problems with two boundaries. II
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1979
SP - 873
EP - 879
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a20/
LA - ru
ID - TVP_1979_24_4_a20
ER -
%0 Journal Article
%A V. I. Lotov
%T Asymptotic analysis of distributions in the problems with two boundaries. II
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 873-879
%V 24
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_4_a20/
%G ru
%F TVP_1979_24_4_a20
Let the conditions of the first part of the paper are satisfied. We obtain the complete asymptotic expansions of the probabilities \begin{gather*} \mathbf P\{S_n=k,\,N>n\},\qquad k\in(-a,b),\\ \mathbf P\{S_N=k,\,N=n\},\qquad k\notin(-a,b), \end{gather*} for the case $a=a(n)=o(n)$, $b=b(n)=o(n)$, $a\to\infty$, $b\to\infty$, $a+b\ge Cn^{1/2}$.
