Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion

For stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H>1/2$, Harnack type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied to the study of existence and uniqueness of invariant measure for a discrete Markov semigroup constructed in terms of the distribution of the solution. Furthermore, we show that entropy-cost inequality holds for the invariant measure