On the stability of mean-field stochastic differential equations with irregular expectation functional

Abstract

In this paper, we consider multidimensional mean-field stochastic differential equations where the coefficients depend on the law in the form of a Lebesgue integral with respect to the measure of the solution. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application for optimal control of diffusions. Namely, we propose a result on the approximation of the solution associated to a relaxed control.