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Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion. (English) Zbl 1327.60120
Summary: In this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter \(H<1/2\). As applications, the strong Feller property, the log-Harnack inequality and the entropy-cost inequality are given. We also get the derivative estimate and give the corresponding Harnack inequality.
MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60G22 Fractional processes, including fractional Brownian motion
34K50 Stochastic functional-differential equations
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