Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations

TL;DR

This paper establishes a large deviation principle for McKean-Vlasov quasilinear SPDEs with small noise, using variational methods without compactness assumptions, applicable to various distribution-dependent equations.

Contribution

It introduces a novel approach to prove the large deviation principle for McKean-Vlasov SPDEs without requiring compactness in the Gelfand triple.

Findings

Proves Laplace principle for McKean-Vlasov SPDEs.

Applicable to stochastic porous media and p-Laplace equations.

Handles both bounded and unbounded domains.

Abstract

This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence criteria to prove the Laplace principle for McKean-Vlasov type SPDEs, which is equivalent to the large deviation principle. Moreover, we do not assume any compactness condition of embedding in the Gelfand triple to handle both the cases of bounded and unbounded domains in applications. The main results can be applied to various McKean-Vlasov type SPDEs such as distribution dependent stochastic porous media type equations and stochastic p-Laplace type equations.