Asymptotics for the distribution of the time of attaining the maximum for a~trajectory of a~Poisson process with linear drift and intensity switch
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 94-109
Voir la notice de l'article provenant de la source Math-Net.Ru
We find the exact asymptotics of the distribution of the time when the
trajectory of the process $Y(t)=at-\nu_+(pt)+\nu_-(-qt)$,
$t\in(-\infty,\infty)$ attains its maximum, where $\nu_{\pm}(t)$ are
independent standard Poisson processes extended by zero on the negative
semiaxis. The parameters $a$, $p$, $q$ are assumed just to satisfy the
condition $\mathbf{E}Y(t)0$, $t\neq 0$.
Keywords:
Poisson process with linear drift, random process with negative mean drift, exact asymptotics of distribution tails.
@article{TVP_2021_66_1_a4,
author = {V. E. Mosyagin},
title = {Asymptotics for the distribution of the time of attaining the maximum for a~trajectory of {a~Poisson} process with linear drift and intensity switch},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {94--109},
publisher = {mathdoc},
volume = {66},
number = {1},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a4/}
}
TY - JOUR AU - V. E. Mosyagin TI - Asymptotics for the distribution of the time of attaining the maximum for a~trajectory of a~Poisson process with linear drift and intensity switch JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2021 SP - 94 EP - 109 VL - 66 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a4/ LA - ru ID - TVP_2021_66_1_a4 ER -
%0 Journal Article %A V. E. Mosyagin %T Asymptotics for the distribution of the time of attaining the maximum for a~trajectory of a~Poisson process with linear drift and intensity switch %J Teoriâ veroâtnostej i ee primeneniâ %D 2021 %P 94-109 %V 66 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a4/ %G ru %F TVP_2021_66_1_a4
V. E. Mosyagin. Asymptotics for the distribution of the time of attaining the maximum for a~trajectory of a~Poisson process with linear drift and intensity switch. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 1, pp. 94-109. http://geodesic.mathdoc.fr/item/TVP_2021_66_1_a4/