Uniform large deviation principles and averaging principles for stochastic Burgers type equations with reflection

TL;DR

This paper establishes uniform large deviation principles and an averaging principle for stochastic Burgers type equations with reflection, providing a comprehensive probabilistic analysis of these complex stochastic PDEs.

Contribution

It introduces uniform large deviation principles for stochastic Burgers equations with reflection and derives an averaging principle using time discretization.

Findings

Proves the Freidlin-Wentzell uniform large deviation principle.

Establishes the Dembo-Zeitouni uniform large deviation principle.

Derives an averaging principle for the equations.

Abstract

This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations uniformly on bounded sets. Then based on this result, we establish the Dembo-Zeitouni uniform large deviation principle for these equations uniformly on compact sets. Finally, an averaging principle result for these equations is obtained through the time discretization approach.