Stochastic evolution equations with multiplicative fractional noise

Abstract

An explicit formula for a solution to stochastic bilinear evolution equation with fractional Gaussian noise has been found. The large time behaviour of solutions has been studied.

Results are applied to stochastic parabolic PDEs with fractional Gaussian noise, in particular, stochastic heat equation.

Keywords

• fractional noise
• stochastic equations in infinite dimensions
• stochastic partial differential equations