Parameter estimation of stochastic differential equation driven by small fractional noise

TL;DR

This paper investigates the asymptotic properties of maximum likelihood estimators for drift parameters in stochastic differential equations driven by small fractional Brownian motion, covering different Hurst index ranges.

Contribution

It provides new theoretical results on the asymptotic normality and convergence of estimators for SDEs driven by small fractional noise, extending existing methods.

Findings

Asymptotic normality of estimators established for H<1/2 and H>1/2

Moment convergence results derived for the estimators

Conditions on the drift coefficient are specified for the results

Abstract

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we obtain the asymptotic normality and moment convergence of maximum likelihood estimator of the drift parameter .