Weak solutions for stochastic differential equations with additive fractional noise

Abstract

We present a new approach to prove the existence of a weak solution for the equation dxt=f(t,xt)dt+g(t)dBtHwhere BtH is a fractional Brownian motion taking values in a separable Hilbert space, and f and g are suitable functions. Our idea involves using the implicit function theorem and the scaling property of the fractional Brownian motion to obtain a weak solution for the equation.