Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts

We study a class of reflected McKean-Vlasov diffusions over convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, process is constrained to (not necessarily bounded) by local time on boundary. These equations include subclass drift towards their mean via convolution solution law stabilizing potential. Firstly, we establish existence and uniqueness results for this address propagation chaos. work broad coefficients, including terms are locally in spatial measure variables. However, rely boundedness or account these non-linearities instead use properties. prove Freidlin-Wentzell type Large Deviations Principle an Eyring-Kramer's exit-time from subdomains contained interior reflecting domain.