Large Deviations for Multi-valued Stochastic Differential Equations

TL;DR

This paper establishes a large deviation principle for multivalued stochastic differential equations with monotone drifts, including reflected SDEs in convex domains, extending the theoretical understanding of their probabilistic behavior.

Contribution

It introduces a large deviation principle for a broad class of multivalued SDEs with monotone drifts, covering reflected cases in convex domains.

Findings

Proves a Freidlin-Wentzell type large deviation principle for multivalued SDEs.

Includes SDEs with reflection in convex domains as a special case.

Extends large deviation theory to more complex stochastic systems.

Abstract

We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.