What question did this study set out to answer?

To study the well-posedness and large deviation principles for multiscale multivalued McKean-Vlasov stochastic systems.

June 11, 2026

Large deviations of multiscale multivalued McKean-Vlasov stochastic systems

Puntos clave

To study the well-posedness and large deviation principles for multiscale multivalued McKean-Vlasov stochastic systems.
Employed contractive mapping principle to establish well-posedness under non-Lipschitz conditions.
Proved a large deviation principle using weak convergence methods for perturbed systems.
Derived two averaging principles as a by-product.
Established the well-posedness of fully coupled multivalued McKean-Vlasov stochastic systems under specific conditions.
Demonstrated a large deviation principle showing how systems behave under small perturbations.
Derived key averaging principles that characterize the systems' long-term behaviors.

Resumen

This work focuses on multiscale multivalued McKean-Vlasov stochastic systems. First, we employ the contractive mapping principle to establish the well-posedness of fully coupled multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Subsequently, for multiscale multivalued McKean-Vlasov stochastic systems perturbed by small noises, we prove a large deviation principle using a weak convergence method. As a by-product, two averaging principles are also derived.

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