Stochastic Affine Evolution Equations with Multiplicative Fractional Noise

Abstract

A stochastic affine evolution equation with bilinear noise term is studied, where the driving process is a real-valued fractional Brownian motion with Hurst parameter greater than 1/2. Stochastic integration is understood in the Skorokhod sense.

The existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained.

Keywords

• geometric fractional Brownian motion
• stochastic differential equations in Hilbert space
• stochastic bilinear equation