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

Abstract

In this paper, the path independent property of additive functionals of McKean–Vlasov stochastic differential equations with jumps is characterized by nonlinear partial integro-differential equations involving [Formula: see text]-derivatives with respect to probability measures introduced by Lions. Our result extends the recent work16 by Ren and Wang where their concerned McKean–Vlasov stochastic differential equations are driven by Brownian motions.