Large deviation principle for stochastic Burgers type equation with reflection

Abstract

<p style='text-indent:20px;'>In this paper, we establish a large deviation principle for stochastic Burgers type equation with reflection perturbed by the small multiplicative noise. The main difficulties come from the highly non-linear coefficient and the singularity caused by the reflection. Here, we adopt a new sufficient condition for the weak convergence criteria, which is proposed by Matoussi, Sabbagh and Zhang [<xref ref-type="bibr" rid="b14">14</xref>].</p>

A Large Deviation Principle for the Stochastic Heat Equation with General Rough Noise

“…In this paper, we adopt a new sufficient condition for the LDP (see Condition 2.8 below) which is proposed by Matoussi, Sabbagh and Zhang [28]. This method has been successfully applied to the study of LDP for SPDEs, see, e.g., [12,14,15,25,35,36]. This paper is organized as follows.…”

Nonlinear stochastic wave equation driven by rough noise

“…In this paper, we adopt a new sufficient condition for the LDP (see Condition 3.5 below) which is proposed by Matoussi, Sabbagh and Zhang [27]. This approach has been proved to be successful in a wide range of SPDEs, see e.g., [15,25,34,35].…”