Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 397-401
Citer cet article
T. P. Miroshnichenko. The optimal stopping of an integral with respect to the Wiener process. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 397-401. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/
@article{TVP_1975_20_2_a14,
author = {T. P. Miroshnichenko},
title = {The optimal stopping of an integral with respect to the {Wiener} process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {397--401},
year = {1975},
volume = {20},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/}
}
TY - JOUR
AU - T. P. Miroshnichenko
TI - The optimal stopping of an integral with respect to the Wiener process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1975
SP - 397
EP - 401
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/
LA - ru
ID - TVP_1975_20_2_a14
ER -
%0 Journal Article
%A T. P. Miroshnichenko
%T The optimal stopping of an integral with respect to the Wiener process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1975
%P 397-401
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/
%G ru
%F TVP_1975_20_2_a14
In this paper an optimal bound is found in the stopping problem, for the Wiener process $W_t$, $0\le t\le1$, with gain $$ V(0,x)=\sup_{0\le\tau\le1}\mathbf M\int_0^\tau(W_s+x)\,ds, $$ where $\tau$ is a Markov time with respect to the family of $\sigma$-algebras $\mathscr F_t^W=\sigma\{W_s,s\le t\}$.
