Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 342-349
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B. A. Rogozin. The distribution of the first hit for stable and asymptotically stable walks on an interval. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 342-349. http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/
@article{TVP_1972_17_2_a9,
author = {B. A. Rogozin},
title = {The distribution of the first hit for stable and asymptotically stable walks on an interval},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {342--349},
year = {1972},
volume = {17},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/}
}
TY - JOUR
AU - B. A. Rogozin
TI - The distribution of the first hit for stable and asymptotically stable walks on an interval
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1972
SP - 342
EP - 349
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/
LA - ru
ID - TVP_1972_17_2_a9
ER -
%0 Journal Article
%A B. A. Rogozin
%T The distribution of the first hit for stable and asymptotically stable walks on an interval
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1972
%P 342-349
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/
%G ru
%F TVP_1972_17_2_a9
Let $\{\xi(t);t\ge0\}$ be a strongly stable process, $\tau=\inf\{t\colon\xi(t)\notin[0,1]\}$. Formulas for $\mathbf P\{1\le\xi(\tau)<1+y\mid\xi(0)=x\}$, and $\mathbf P\{0\ge\xi(\tau)>-y\mid\xi(0)=x\}$, $0\le x\le1$, $y\ge0$, are derived and applied to random walks.
