Некоторые теоремы типа восстановления
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 585-601
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Let $F(x)$ be a distribution function with $F(0)=0$ and $$ H(x,A)=\sum_{k=0}^\infty A^kF_k(x),\quad A>0, $$ where $F_k(x)$, $k\ge1$, is the $k$-th convolution of $F(x)$ and $F_0(x)$ is the degenerate distribution function with the unit jump at $x=0$. In the paper the asymptotic behaviour of $H(x,A)-H(x-l,A)$ is studied. The dominant term and an estimate for the remainder are obtained, $F(x)$ being assumed1) to be of the lattice type or to have a non-zero absolutely continuous component and2) to have a finite number of moments or to satisty well-known Cramér's condition.
@article{TVP_1968_13_4_a0,
author = {S. V. Nagaev},
title = {{\CYRN}{\cyre}{\cyrk}{\cyro}{\cyrt}{\cyro}{\cyrr}{\cyrery}{\cyre} {\cyrt}{\cyre}{\cyro}{\cyrr}{\cyre}{\cyrm}{\cyrery} {\cyrt}{\cyri}{\cyrp}{\cyra} {\cyrv}{\cyro}{\cyrs}{\cyrs}{\cyrt}{\cyra}{\cyrn}{\cyro}{\cyrv}{\cyrl}{\cyre}{\cyrn}{\cyri}{\cyrya}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {585--601},
year = {1968},
volume = {13},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a0/}
}
S. V. Nagaev. Некоторые теоремы типа восстановления. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 585-601. http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a0/