Stochastic partial differential equation with reflection driven by fractional noises

ABSTRACT

In this paper, we focus on a reflected parabolic stochastic partial differential equation driven by fractional noises and reflected at zero. First we study the existence and uniqueness of the solution, then we obtain its large deviation principle via a typical method of Azencott.

KEYWORDS:

• Reflected stochastic partial differential equation
• fractional Brownian motion
• large deviation principle

AMS SUBJECT CLASSIFICATIONS:

• 35R60
• 60H15

Additional information

Funding

S. Wang is supported by the China Scholarship Council (CSC File No. 201807315008), the National Natural Science Foundation of China (Grant No. 11501565) and the Youth Project of Humanities and Social Sciences of Ministry of Education (Grant No. 19YJCZH251). Y. Jiang (the corresponding author) is supported by National Natural Science Foundation of China (Grant No. 11571190) and the Fundamental Research Funds for the Central Universities.