Large deviation principles for fully coupled multiscale multivalued stochastic systems

TL;DR

This paper establishes large deviation principles for fully coupled multiscale multivalued stochastic systems, using viscosity solutions of Hamilton-Jacobi-Bellman equations, and demonstrates the results with a concrete example.

Contribution

It introduces a novel approach to analyze large deviations in complex multiscale multivalued stochastic systems using viscosity solutions.

Findings

Large deviation principles are proven for the slow component.

Theoretical results are validated through a concrete example.

Abstract

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a general stochastic differential equation. First, we establish the large deviation principle for the slow component at any fixed time by leveraging viscosity solutions of second-order Hamilton-Jacobi-Bellman equations involving multivalued operators. Subsequently, we illustrate the theoretical results through a concrete example.