Exact maximum likelihood estimators for drift fractional Brownian motions

TL;DR

This paper investigates the properties of maximum likelihood estimators for the mean and variance of drift fractional Brownian motions observed discretely, establishing their consistency, strong consistency, and a central limit theorem using Malliavin calculus.

Contribution

It provides the first rigorous analysis of the asymptotic behavior of MLEs for drift fractional Brownian motions, including consistency and distributional limits.

Findings

MLEs are consistent and strongly consistent for drift fractional Brownian motions.

A central limit theorem for the estimators is established.

The analysis employs Malliavin calculus techniques.

Abstract

This paper deals with the problems of consistence and strong consistence of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. A central limit theorem for these estimators is also obtained by using the Malliavin calculus.