Stochastic bilinear equations with fractional Gaussian noise in Hilbert space

Abstract

A fractional Gaussian noise is a formal derivative of a fractional Brownian motion. An explicit formula for a weak solution to the stochastic billinear equation in a separable Hilbert space with fractional Gaussian noise in the singular case $H\in (0,1/2)$ is given.

The stochastic integral is understood in the Skorokhod sense.

Keywords

• fractional Brownian motion
• stochastic differential equations in Hilbert space
• explicit formula for solution