Local exponential stability for SDE's driven by an fbm with Hurst parameter in $(1/3,1/2]$

We formulate conditions for existence and uniqueness for SDE's driven by an fbm with Hurst parameter in $(1/3,1/2]$. We then prove that under particular conditions on the coefficients of this equation for initial conditions in a random neighborhood of zero the solution converges exponentially fast to the trivial solution.