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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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