Stability for Multivalued McKean–Vlasov Stochastic Differential Equations

Abstract

The work concerns multivalued McKean–Vlasov stochastic differential equations. First of all, we prove the existence and uniqueness of strong solutions for multivalued McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients. Then, the classical Itô’s formula is extended to that for multivalued McKean–Vlasov stochastic differential equations. Finally, the asymptotic stability of second moments and the almost surely asymptotic stability for their solutions in terms of a Lyapunov function are shown.

Keywords

Multivalued McKean–Vlasov stochastic differential equations / the generalized Itô formula / the asymptotic stability of second moments / the almost surely asymptotic stability

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Peking University