Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 146-149
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A. V. Mel'nikov. On the strong solutions of stochastic differential equations with nonsmooth coefficients. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 146-149. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/
@article{TVP_1979_24_1_a10,
author = {A. V. Mel'nikov},
title = {On the strong solutions of stochastic differential equations with nonsmooth coefficients},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {146--149},
year = {1979},
volume = {24},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/}
}
TY - JOUR
AU - A. V. Mel'nikov
TI - On the strong solutions of stochastic differential equations with nonsmooth coefficients
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1979
SP - 146
EP - 149
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/
LA - ru
ID - TVP_1979_24_1_a10
ER -
%0 Journal Article
%A A. V. Mel'nikov
%T On the strong solutions of stochastic differential equations with nonsmooth coefficients
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 146-149
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a10/
%G ru
%F TVP_1979_24_1_a10
By means of purely probabilistic methods we prove the existence of strong solution of a stochastic differential equation $$ dx(t,\omega)=f(x(t,\omega))\,dt+dw(t,\omega),x(0,\omega)=x_0\in R^1,\ 0\le t\le T<\infty, $$ in the case when the drift coefficient $f(x)$ is bounded and piecewise smooth or continuous function.
