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Harnack-type inequalities and applications for SDE driven by fractional Brownian motion. (English) Zbl 1304.60072
The author establishes Harnack-type inequalities for stochastic differential equations driven by fractional Brownian motion with Hurst parameter \(H> \frac12\). The inequalities are obtained directly, using a technique to construct a coupling with unbounded time-dependent drift. Using also a Girsanov transformations argument, the dimension-free Harnack-type inequalities and the strong Feller property are proved. In terms of the distribution, the author builds a discrete Markov semigroup. Moreover, the existence and uniqueness of an invariant probability measure for the corresponding semigroup is proved, and its entropy-cost inequality is established.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
47D07 Markov semigroups and applications to diffusion processes
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