Moderate deviations for a class of semilinear SPDE with fractional noises

Abstract

Let $C^{\beta }([0,T]\times [0,1])$ denote the set of functions which are β-Hölder continuous in t and $2\beta$-Hölder continuous in x with $0<\beta <\frac{1}{2}\left(H_2+\frac{\alpha }{2}-1\right),1/2<H_2<1$ and $1<\alpha <2.$ In this article, we prove a large deviation principles in $C^{\beta }([0,T]\times [0,1])$ 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.

Keywords:

• Stochastic partial differential equations
• fractional noises
• large deviation principle
• moderate deviations principle
• central limit theorem

2010 AMS Classification Numbers:

• 60H15
• 60F05
• 60F10

Additional information

Funding

Partially supported by Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 18YJCZH101), Natural Science Foundation of Jiangsu Province of China (No. BK20161579), Major Research Plan of Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 18KJA110002), QingLan Project and 333 Talent Training Project of Jiangsu Province (No. BRA2018357).