Local linear estimator for fractional diffusions

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.