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

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.