## 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.

### MSC:

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