Reflected SPDEs driven by fractional noises
The authors study a stochastic partial differential equation (SPDE) with two reflecting smooth barriers. The equation is driven by an additive fractional noise, which is fractional in time and white in space. One purpose of the paper is to obtain the existence and uniqueness of the solution of SPDE and its Hölder continuity with respect to the time and space variables. Another goal is to establish a large deviation principle for the solution of the SPDE of such type but with a small noise. The main approach to obtaining the large deviation principle is to prove the regularity of the skeleton and to combine it with the Freidlin-Wentzell inequality.
stochastic partial differential equations with two reflecting walls
scientific article; zbMATH DE number 7189528
scientific article