McKean-Vlasov stochastic variational inequalities with oblique subgradients and propagation of chaos

This work addresses the problem of existence and uniqueness of solutions for a type of McKean-Vlasov stochastic variational inequalities with oblique subgradients, where the coefficients depend on the distribution of the state process. To construct the solution, we employ two methods under different conditions: the Moreau-Yosida approximation and the tightness criteria. As an application, we study a special approximation for the solution ($ X,A $), known as the propagation of chaos, through the solutions ($ X^N,A^N $) of a weakly interacting $ N $-particle system, the coefficients of which depend on the empirical distribution of the system.