Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data

TL;DR

This paper extends the large deviations principles for stochastic reaction-diffusion systems to more general settings, including unbounded initial data, facilitating analysis of exit times and shapes.

Contribution

It proves uniform large deviations results for stochastic reaction-diffusion equations in broader contexts than previous work, including unbounded initial data scenarios.

Findings

Large deviations principles are established for more general reaction-diffusion systems.

Uniformity over unbounded initial data sets is achieved in certain common situations.

Facilitates analysis of exit times and shapes from unbounded sets.

Abstract

Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over bounded sets of initial data. This paper proves uniform large deviations results for a system of stochastic reaction--diffusion equations in a more general setting than Cerrai and Rockner. Furthermore, this paper identifies two common situations where the large deviations principle is uniform over unbounded sets of initial data, enabling the characterization of Freidlin-Wentzell exit time and exit shape asymptotics from unbounded sets.