Large deviations for invariant measures of multivalued stochastic differential equations with jumps

TL;DR

This paper establishes large deviation principles for invariant measures of multivalued stochastic differential equations with jumps, providing bounds that deepen understanding of their probabilistic behavior.

Contribution

It introduces the first large deviation principles for invariant measures of multivalued SDEs with jumps using the weak convergence approach.

Findings

Proved Freidlin-Wentzell and Dembo-Zeitouni large deviation principles

Derived upper and lower bounds for invariant measures' large deviations

Enhanced understanding of probabilistic behavior of multivalued SDEs with jumps

Abstract

This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large deviation principle for these equations. Subsequently, based on these results, we derive both upper and lower bounds for the large deviations of invariant measures associated with the equations.