The stability and path-independence of additive functionals for multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients

Jun Gong, Huijie Qiao

Published 2021-06-22Version 1

The work concerns the stability and path-independence of additive functionals for a type of multivalued McKean-Vlasov stochastic differential equations with non-Lipschitz coefficients. First, we prove the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equation with non-Lipschitz coefficients. And then, the exponential stability of second moments for their solutions in terms of a Lyapunov function is shown. Next, we weaken the conditions and furthermore obtain the exponentially 2-ultimate boundedness of their solutions. Finally, the path-independence of additive functionals for their solutions is proved.