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Integration by Parts Formulas of Mckean-Vlasov SDEs with Jumps and Some Applications
Yao Chen, Jiagang Ren, Hua Zhang · 2026-05-20 · via math.PR updates on arXiv.org

In this article, we establish integration by parts formulas for the solutions of McKean-Vlasov stochastic differential equations with jumps under elliptic coefficients. The derived formulas accommodate both derivatives with respect to real-valued variables and measure-valued variables, interpreted through the Lions' derivative. As applications, we obtain estimates for the derivatives of the density functions of the McKean-Vlasov SDEs, and relying on the integration by parts formulas, we subsequently prove the existence and uniqueness of classical solutions to the associated PDEs with irregular terminal conditions.

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