Geodesic
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. 
@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},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a4/}
}
TY  - JOUR
AU  - A. S. Cherny
TI  - On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2001
SP  - 483
EP  - 497
VL  - 46
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a4/
LA  - ru
ID  - TVP_2001_46_3_a4
ER  - 
%0 Journal Article
%A A. S. Cherny
%T On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2001
%P 483-497
%V 46
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a4/
%G ru
%F TVP_2001_46_3_a4
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/