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.

23 pages

References in corpus (1)

• Path independence of the additive functionals for McKean-Vlasov stochastic differential equations with jumps