Bismut Formula for Intrinsic Derivative of DDSDEs with Singular Interactions

In recent years, remarkable progress has been made for Distribution dependent stochastic equations (DDSDEs) with singular interactions, existing results include wellposedness, propagation of chaos, entropy cost inequality and ergodicity. As a continuation to the existing study, in this paper we establish Bismut type formulas for the intrinsic derivative of DDSDEs with singular interactions, which extends the existing formula established for the case with Lion’s differentiable drifts.