Large deviations of multiscale multivalued McKean-Vlasov stochastic systems

TL;DR

This paper establishes well-posedness and large deviation principles for multiscale multivalued McKean-Vlasov stochastic systems, introducing new methods for systems with non-Lipschitz conditions and small noise effects.

Contribution

It provides the first well-posedness results under non-Lipschitz conditions and proves a large deviation principle using weak convergence for these complex systems.

Findings

Well-posedness under non-Lipschitz conditions

Large deviation principle for small noise systems

Two averaging principles derived

Abstract

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Then for multiscale multivalued McKean-Vlasov stochastic systems with small noises, we prove a large deviation principle by a weak convergence approach. As a by-product, two averaging principles are obtained.