Stability and prevalence of McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients

Mohamed Amine Mezerdi (1, 2) , Nabil Khelfallah (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 BISKRA - Université Mohamed Khider de Biskra

Abstract We consider various approximation properties for systems driven by a McKean–Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations is stable with respect to small perturbation of initial conditions, parameters and driving processes. Moreover, the unique strong solutions may be constructed by an effective approximation procedure. Finally, we show that the set of bounded uniformly continuous coefficients for which the corresponding MVSDE have a unique strong solution is a set of second category in the sense of Baire.

Domaines: Mathématiques [math]

Mohamed Amine Mezerdi, Nabil Khelfallah. Stability and prevalence of McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients. Random Operators and Stochastic Equations, 2021, 29 (1), pp.67-78. ⟨10.1515/rose-2021-2053⟩. ⟨hal-03498283⟩