Abstract
Let denote the set of functions which are β-Hölder continuous in t and
-Hölder continuous in x with
and
In this article, we prove a large deviation principles in
for the solution to a class of stochastic semilinear equation arising from 1-dimension integro-differential scalar conservation laws. The equation is driven by a double-parameter fractional noise. In addition, we also prove a central limit theorem and establish a moderate deviation principle for the same stochastic partial differential equation.