On a general approach to Freidlin-Wentzell exit problems for stochastic equations in Banach spaces

TL;DR

This paper introduces a general control-theoretic method to analyze exit times and locations for a broad class of stochastic equations in Banach spaces, extending classical finite-dimensional results to infinite-dimensional settings.

Contribution

It develops a unified approach for exit problems in infinite-dimensional stochastic systems, generalizing Freidlin-Wentzell theory beyond specific models.

Findings

Establishes a general framework for exit time asymptotics in Banach spaces.

Provides new results on exit locations for infinite-dimensional stochastic equations.

Extends classical finite-dimensional exit problem results to Banach space settings.

Abstract

Freidlin and Wentzell characterized the logarithmic asymptotics of the exit time from a basin of attraction for a finite dimensional diffusion with small noise. After that, several authors studied the same properties for exit problems associated to specific infinite dimensional system. In this paper, we present a general method, based a control theoretic approach, to establish exit time and exit place results for a large class of stochastic equations in Banach spaces.