A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2

Abstract

Given a fractional Brownian motion \,\,$(B_t^H{)}_{t\ge 0}$,\, with Hurst parameter \,$>1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u}dμ(u), \;\; 0\leq t\leq 1{equation} A different stochastic calculus is required for the process because it is not a semimartingale.