McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

TL;DR

This paper establishes well-posedness and large deviation principles for McKean-Vlasov SPDEs driven by Poisson measures, extending existing theories to unbounded domains and specific equations like stochastic porous media.

Contribution

It adapts the variational framework and weak convergence approach to prove results for McKean-Vlasov SPDEs with monotone coefficients, including unbounded domain cases.

Findings

Proved well-posedness of McKean-Vlasov SPDEs with Poisson noise.

Established large deviation principles for these equations.

Extended applicability to unbounded domains without compactness assumptions.

Abstract

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic p-Laplace equation. Our proof is based on the weak convergence approach introduced by Budhiraja et al. for Poisson random measures, the time discretization procedure and relative entropy estimates. In particular, we succeed in dropping the compactness assumption of embedding in the Gelfand triple in order to deal with the case of bounded and unbounded domains in applications.