A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >12

Given a fractional Brownian motion (BtH)t≥0, with Hurst parameter >12, we study the properties of all solutions of equation(1)Xt=BtH+∫0tXudμ(u),0≤t≤1. A different stochastic calculus is required for the process because it is not a semimartingale.