Large Deviation Principle for Stochastic Generalized KdV Equation with Additive Noise

Abstract

The aim of this work is to prove the large deviation principle for the law of solutions of a stochastic generalised Korteweg-de Vries (gKdV) equation subject to a small additive noise. The large deviation analysis is based on the variational representation for Polish space-valued functionals of an infinite dimensional Brownian motion. The essence of the proof relies on the weak convergence approach put forward by Budhiraja, Dupuis, and Maroulas that suffices to prove the uniform Laplace principle.