Weak solutions for stochastic differential equations with additive fractional noise

We give a new approach to prove the existence of a weak solution of $$d{x}_t=f(t,x_t)dt+g(t)d{B}_t^H$$ where $B_t^H$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property of the fractional Brownian motion in order to obtain a weak solution for this equation.