Abstract
In this paper, we investigate the nonparametric local linear estimator for the drift function of stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter [Formula: see text]. The drift function is one-sided dissipative Lipschitz that ensures the ergodic property of the SDE. We derive the strong consistency of the proposed estimator with proper bandwidth selectors associated with the determined Hurst parameter [Formula: see text]. The main tools are the ergodic theorem, Malliavin calculus, and a maximum inequality for It[Formula: see text]–Skorohod integrals.
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