Geodesic
On pathwise uniqueness of solutions for multidimensional McKean--Vlasov equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 581-588

Voir la notice de l'article provenant de la source Math-Net.Ru

Pathwise uniqueness for the multidimensional stochastic McKean–Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the solution. It is assumed that both coefficients are bounded, and, moreover, the drift is Dini-continuous in the state variable, and the diffusion satisfies the Lipschitz condition and is also continuous in time and uniformly nondegenerate. This is the classical McKean–Vlasov setting, that is, the coefficients of the equation are represented as integrals over the marginal distributions of the process.
Keywords: McKean–Vlasov's equation, strong uniqueness. 
@article{TVP_2021_66_3_a9,
     author = {A. Yu. Veretennikov},
     title = {On pathwise uniqueness of solutions for multidimensional {McKean--Vlasov} equation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {581--588},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a9/}
}
TY  - JOUR
AU  - A. Yu. Veretennikov
TI  - On pathwise uniqueness of solutions for multidimensional McKean--Vlasov equation
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 581
EP  - 588
VL  - 66
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a9/
LA  - ru
ID  - TVP_2021_66_3_a9
ER  - 
%0 Journal Article
%A A. Yu. Veretennikov
%T On pathwise uniqueness of solutions for multidimensional McKean--Vlasov equation
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 581-588
%V 66
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a9/
%G ru
%F TVP_2021_66_3_a9
A. Yu. Veretennikov. On pathwise uniqueness of solutions for multidimensional McKean--Vlasov equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 581-588. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a9/