Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 458-465
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A. A. Novikov. On stopping times for the Wiener process. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 458-465. http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a3/
@article{TVP_1971_16_3_a3,
author = {A. A. Novikov},
title = {On stopping times for the {Wiener} process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {458--465},
year = {1971},
volume = {16},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a3/}
}
TY - JOUR
AU - A. A. Novikov
TI - On stopping times for the Wiener process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1971
SP - 458
EP - 465
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a3/
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ID - TVP_1971_16_3_a3
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%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
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%N 3
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%G ru
%F TVP_1971_16_3_a3
In the paper, the expectations $\mathbf M(\tau(a,b,c)+c)^\nu$, $-\infty<\nu<\infty$, are found where $\tau(a,b,c)$ is the first passage time of the Wiener process for a one-side bound $a+b(t+c)^{1/2}$. A moment identity for stochastic integrals is proved which can be useful when studying the properties of Markov times.