Nonparametric Estimation in Fractional SDE

Abstract

This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via both some long-time behavior properties of Hairer and some properties of the Skorokhod integral with respect to the fractional Brownian motion. These results are illustrated on the fractional Ornstein-Uhlenbeck process.

21 pages

References in corpus (2)

• Statistical aspects of the fractional stochastic calculus
• Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion

Cited by in corpus (7)

• A general drift estimation procedure for stochastic differential equations with additive fractional noise
• Nonparametric Estimation for I.I.D. Paths of Fractional SDE
• Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application
• On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE
• Nonparametric Estimation of the Trend in Reflected Fractional SDE
• On a Calculable Skorokhod's Integral Based Projection Estimator of the Drift Function in Fractional SDE
• Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion