Some Solutions of Semilinear Stochastic Equations in a Hilbert Space With a Fractional Brownian Motion

Stochastic equations in a Hilbert space with a fractional Brownian motion are used to model stochastic partial differential equations with a space-time noise. Some semilinear stochastic equations are shown to possess one and only one weak solution. These weak solutions are constructed from the solutions of the corresponding linear equations by an absolutely continuous transformation of measures. Some examples of stochastic differential and partial differential equations are given to demonstrate the applicability of the results