Well-posedness and propagation of chaos for McKean-Vlasov stochastic variational inequalities

In this paper, we study a broad class of McKean-Vlasov stochastic variational inequalities (MVSVIs), where both the drift coefficient b and the diffusion coefficient depend on time t, the state Xₜ and its distribution ₜ. We establish the strong well-posedness, when b is superlinear growth and locally Lipschitz continuous, and is locally H\"older continuous, both with respect to Xₜ and ₜ. Additionally, we present the first propagation of chaos result for MVSVIs.