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

TL;DR

This paper characterizes the path independence of additive functionals in McKean-Vlasov SDEs with jumps using nonlinear partial integro-differential equations involving L-derivatives, extending previous Brownian motion results.

Contribution

It extends the characterization of path independence to McKean-Vlasov SDEs with jumps using L-derivatives, generalizing prior Brownian motion-based work.

Findings

Path independence characterized by nonlinear PDEs with L-derivatives.

Extension of previous Brownian motion results to jump processes.

Provides a theoretical framework for additive functionals in jump-driven McKean-Vlasov SDEs.

Abstract

In this article, the path independent property of additive functionals of McKean-Vlasov stochastic differential equations with jumps is characterised by nonlinear partial integro-differential equations involving $L$-derivatives with respect to probability measures introduced by P.-L. Lions. Our result extends the recent work [16] by Ren and Wang where their concerned McKean-Vlasov stochastic differential equations are driven by Brownian motions.