Weak solutions for stochastic differential equations with additive fractional noise

We give a new approach to prove the existence of a weak solution of $dx_t = f(t,x_t)dt + g(t)dB^H_t$ where $B^H_t$ 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.

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