On the support of the solutions of stochastic differential equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 649-653
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Let $x=(x(t))_{t\ge 0}$ be a solution of stochastic differential equation (1.1m) generated by a continuous semimartingale and let $x^\omega=(x^\omega(t))_{t\ge 0}$ be a solution of ordinary differential equation (1.1w) generated by absolutely continuous functions The paper generalizing the Strook and Varadhan result [15] shows that the topological support of distributions of the process $(x(t))_{t\ge 0}$ coincides with the closure of the solutions set $\{X^\omega:\omega \text{ are absolutely continuous functions }\}$.
Keywords:
stochastic and ordinary differential equations, topological support of distributions of a process, strong solutions of stochastic equations, semimartingales.
@article{TVP_1994_39_3_a13,
author = {I. Gy\"ongy},
title = {On the support of the solutions of stochastic differential equations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {649--653},
publisher = {mathdoc},
volume = {39},
number = {3},
year = {1994},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a13/}
}
I. Gyöngy. On the support of the solutions of stochastic differential equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 649-653. http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a13/