  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.
