Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 685-701
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A. Ju. Veretennikov. On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 685-701. http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/
@article{TVP_1981_26_4_a1,
author = {A. Ju. Veretennikov},
title = {On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {685--701},
year = {1981},
volume = {26},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/}
}
TY - JOUR
AU - A. Ju. Veretennikov
TI - On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1981
SP - 685
EP - 701
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/
LA - ru
ID - TVP_1981_26_4_a1
ER -
%0 Journal Article
%A A. Ju. Veretennikov
%T On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 685-701
%V 26
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a1/
%G ru
%F TVP_1981_26_4_a1
We investigate the sufficient conditions for the strong and weak uniqueness of the solution of a stochastic equation with a simultaneous reflection at zero: \begin{gather*} dx_s=\sigma(s,x_s)\,dw_s+b(s,x_s)\,ds+d\varphi_s, \\ d\varphi_s=\chi_{x_s=0}\,d\varphi_s,\qquad x_s\ge 0, \end{gather*} and for the existence of a strong solution of this equation.
