Small noise and small time asymptotics for McKean–Vlasov SDEs with local Lipschitz coefficients

This work is mainly concerned with small noise and small time asymptotics for a class of McKean–Vlasov stochastic differential equations with local Lipschitz coefficients. We apply the modified weak convergence criteria to prove the Laplace principle (equivalently, the large deviation principle). The main results extend the existing ones to the case of fully local assumptions with respect to both the state and measure variables in the literature. As a consequence, the small time asymptotics for McKean–Vlasov SDEs are also derived.