Mean reflected Mckean-Vlasov stochastic differential equation

Abstract

In this paper, we investigate a class of mean reflected McKean-Vlasov stochastic differential equation, which extends the equation proposed by [1] by allowing the solution's distribution to not only constrain its behavior, but also affect the diffusion and drift coefficients. We establish the existence and uniqueness results of this class, investigate the propagation of chaos, and examine the stability properties with respect to the initial condition, coefficients, and driving process. Moreover, we provide a rigorous proof of a Fredlin-Wentzell type large deviations principle using the weak convergence method. We also demonstrate the existence of an invariant measure and employ the coupling by change of measure method to prove log-Harnack inequality and shift Harnack inequality. Our study sheds light on the properties and behaviors of these reflected Mckean-Vlasov stochastic differential equation and contributes to the ongoing research in this field.