Stochastic bilinear equations with fractional Gaussian noise in Hilbert space. (English) Zbl 1229.60073

Summary: 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 \(H<1/2\) is given. The stochastic integral is understood in the Skorokhod sense.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion