Large deviations of multiscale multivalued McKean-Vlasov stochastic systems

Key Points

• 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.