Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 116-128
Citer cet article
V. R. Khodzhibaev. Asymptotic Representations for Characteristics of Exit from an Interval for Stochastic Processes with Independent Increments. Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 116-128. http://geodesic.mathdoc.fr/item/MT_1998_1_1_a4/
@article{MT_1998_1_1_a4,
author = {V. R. Khodzhibaev},
title = {Asymptotic {Representations} for {Characteristics} of {Exit} from {an~Interval} for {Stochastic} {Processes} with {Independent} {Increments}},
journal = {Matemati\v{c}eskie trudy},
pages = {116--128},
year = {1998},
volume = {1},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_1998_1_1_a4/}
}
TY - JOUR
AU - V. R. Khodzhibaev
TI - Asymptotic Representations for Characteristics of Exit from an Interval for Stochastic Processes with Independent Increments
JO - Matematičeskie trudy
PY - 1998
SP - 116
EP - 128
VL - 1
IS - 1
UR - http://geodesic.mathdoc.fr/item/MT_1998_1_1_a4/
LA - ru
ID - MT_1998_1_1_a4
ER -
%0 Journal Article
%A V. R. Khodzhibaev
%T Asymptotic Representations for Characteristics of Exit from an Interval for Stochastic Processes with Independent Increments
%J Matematičeskie trudy
%D 1998
%P 116-128
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/MT_1998_1_1_a4/
%G ru
%F MT_1998_1_1_a4
Given a homogeneous process $\xi(t)$ with independent increments, we consider the random variables $T=\inf\bigl\{t:\xi(t)\notin[-a,b]\bigr\}$ ($a\ge 0$, $b>0$) and $\xi(T)$, as well as $\theta$, the first passage time across the level $b$ by the process $\xi(t)-a-\min\Bigl\{-a,\ \inf\limits_{s\le t}\xi(s)\Bigr\}$. We find asymptotic expansions for the distribution $\xi(T)$ and for $\mathbb E T$ and $\mathbb E\theta$ as $b\to\infty$.
