On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 483-497
Voir la notice de l'article provenant de la source Math-Net.Ru
We prove that the uniqueness in law for an SDE \begin{equation} dX_t^i=b_t^i(X)\,dt+\sum_{j=1}^m\sigma_t^{ij}(X)\,dB_t^j, \qquad X_0^i=x^i,\quad i=1,\dots,n,\quad \tag{1} \end{equation} implies the uniqueness of the joint distribution of a pair $(X,B)$. Moreover, we prove that the uniqueness in law for (1), together with the strong existence, guarantees the pathwise uniqueness. This result is somehow “dual” to the theorem of Yamada and Watanabe.
Keywords:
stochastic differential equations, weak solutions, strong solutions, uniqueness in law, pathwise uniqueness, theorem of Yamada and Watanabe.
A. S. Cherny. On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 483-497. http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a4/
@article{TVP_2001_46_3_a4,
author = {A. S. Cherny},
title = {On the {Uniqueness} in {Law} and the {Pathwise} {Uniqueness} for {Stochastic} {Differential} {Equations}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {483--497},
year = {2001},
volume = {46},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a4/}
}