On the convergence of carathéodory numerical scheme for Mckean-Vlasov equations

Mohamed Amine Mezerdi (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

We study the strong convergence of the Carathéodory numerical scheme for a class of nonlinear McKean-Vlasov stochastic differential equations (MVSDE). We prove, under Lipschitz assumptions, the convergence of the approximate solutions to the unique solution of the MVSDE. Moreover, we show that the result remains valid, under continuous coefficients, provided that pathwise uniqueness holds. The proof is based on weak convergence techniques and the Skorokhod embedding theorem. In particular, this general result allows us to construct the unique strong solution of a MVSDE by using the Carathéodory numerical scheme. Examples under which pathwise uniqueness holds are given.

Mots clés: McKean-Vlasov equation; mean-field equation; carathéodory numerical scheme; wasserstein distance; delay equation; tightness; pathwise uniqueness; strong solution

Domaines: Mathématiques [math]

Mohamed Amine Mezerdi. On the convergence of carathéodory numerical scheme for Mckean-Vlasov equations. Stochastic Analysis and Applications, 2020, 39 (5), pp.804-818. ⟨10.1080/07362994.2020.1845206⟩. ⟨hal-03498284⟩