Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 845-851
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G. Š. Lev. Asymptotic properties of the extinction probability for a Markov multiplication process. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 845-851. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/
@article{TVP_1977_22_4_a15,
author = {G. \v{S}. Lev},
title = {Asymptotic properties of the extinction probability for {a~Markov} multiplication process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {845--851},
year = {1977},
volume = {22},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/}
}
TY - JOUR
AU - G. Š. Lev
TI - Asymptotic properties of the extinction probability for a Markov multiplication process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1977
SP - 845
EP - 851
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/
LA - ru
ID - TVP_1977_22_4_a15
ER -
%0 Journal Article
%A G. Š. Lev
%T Asymptotic properties of the extinction probability for a Markov multiplication process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1977
%P 845-851
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a15/
%G ru
%F TVP_1977_22_4_a15
For sequences $\{\tau_i\}$, $\{\gamma_i\}$ of independent positive random variables the following process is constructed: $Y(0)=x$, $dY/dt=-1$ everywhere except points $t_n=\tau_1+\dots+\tau_n$ where $Y(t_n)=\gamma_n Y(t_n-0)=Y(t_n+0)$. Limit theorems are proved concerning the behaviour of the extinction probability $$ f(x)=\mathbf P(\inf\{Y(t),t\ge 0\}<0),\qquad x\to\infty. $$
