Li, Zhi; Luo, Jiaowan Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion. (English) Zbl 1327.60120 Random Oper. Stoch. Equ. 22, No. 4, 213-226 (2014). 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 Keywords:functional stochastic differential equations; Harnack inequalities; fractional Brownian motion; strong Feller property PDFBibTeX XMLCite \textit{Z. Li} and \textit{J. Luo}, Random Oper. Stoch. Equ. 22, No. 4, 213--226 (2014; Zbl 1327.60120) Full Text: DOI