We give a new approach to prove the existence of a weak solution of dxtβ=f(t,xtβ)dt+g(t)dBtHβ where BtHβ 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.Comment: 10page