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Harnack inequality and applications for stochastic retarded differential equations driven by fractional Brownian motion. (English) Zbl 1389.60066
Summary: In this paper, by using a semimartingale approximation of a fractional stochastic integration, the global Harnack inequalities for stochastic retarded differential equations driven by fractional Brownian motion with Hurst parameter $$0 < H < 1$$ are established. As applications, the strong Feller property, the log-Harnack inequality and the entropy cost inequality are given.
MSC:
 60H05 Stochastic integrals 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60G22 Fractional processes, including fractional Brownian motion
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