Nonparametric Estimation for Stochastic Differential Equations Driven by Fractional Brownian Motion

TL;DR

This paper develops a nonparametric estimator for the drift function of ergodic stochastic differential equations driven by fractional Brownian motion, demonstrating its consistency based on ergodic properties and stochastic integrals.

Contribution

It introduces a novel nonparametric Nadaraya-Watson estimator for fractional Brownian motion-driven SDEs and proves its consistency using ergodic theory.

Findings

Estimator is consistent for H > 1/2

Works with discretely observed data

Applicable to ergodic fractional SDEs

Abstract

We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic processes. By using the ergodic properties and stochastic integral, we obtain the consistency of the proposed estimator.