Stochastic affine evolution equations with multiplicative fractional noise

[摘要] 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.

[学科分类] 应用数学

[关键词] geometric fractional Brownian motion;stochastic differential equations in Hilbert space;stochastic bilinear equation