Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 159-163
Citer cet article
A. I. Fokht. On the distribution of the first jump over a high barrier for a generalized Poisson process with drift. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 159-163. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/
@article{TVP_1974_19_1_a13,
author = {A. I. Fokht},
title = {On the distribution of the first jump over a~high barrier for a~generalized {Poisson} process with drift},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {159--163},
year = {1974},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/}
}
TY - JOUR
AU - A. I. Fokht
TI - On the distribution of the first jump over a high barrier for a generalized Poisson process with drift
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 159
EP - 163
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/
LA - ru
ID - TVP_1974_19_1_a13
ER -
%0 Journal Article
%A A. I. Fokht
%T On the distribution of the first jump over a high barrier for a generalized Poisson process with drift
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 159-163
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/
%G ru
%F TVP_1974_19_1_a13
Let $\xi(t)$ be a process with independent increments and finite number of jumps. Define $\eta_x=\inf\{t\colon\xi(t)\ge x\}$ and $\chi_x=\xi(\eta_x)-x(x>0)$. For the limit distribution $$ \lim_{x\to\infty}\mathbf P\{\chi_x\le x\} $$ explicit expresions are given.
