Large and Moderate deviation principles for the Multivalued McKean-Vlasov SDEs with jumps

TL;DR

This paper establishes large and moderate deviation principles for multivalued McKean-Vlasov SDEs with jumps driven by Lévy noise, using weak convergence and Bihari's inequality to handle non-Lipschitz coefficients.

Contribution

It introduces a novel approach to analyze deviations in complex stochastic differential equations with non-Lipschitz coefficients and jumps.

Findings

Proved large deviation principles for multivalued McKean-Vlasov SDEs with Lévy noise.

Established moderate deviation principles under non-Lipschitz conditions.

Applied Bihari's inequality to address non-Lipschitz challenges.

Abstract

By using the weak convergence method, we establish the large and moderate deviation principles for the multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients driven by L\'{e}vy noise in this paper. The Bihari's inequality is used to overcome the challenges arising from the non-Lipschitz conditions on the coefficients.