On drift parameter estimation in models with fractional Brownian motion
Probability
2011-12-13 v1 Methodology
Abstract
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard estimates and three estimates for the sequential estimation. Model strong consistency and some other properties are proved. The linear model and Ornstein-Uhlenbeck model are studied in detail. As an auxiliary result, an asymptotic behavior of the fractional derivative of the fractional Brownian motion is established.
Cite
@article{arxiv.1112.2330,
title = {On drift parameter estimation in models with fractional Brownian motion},
author = {Yuriy Kozachenko and Alexander Melnikov and Yuliya Mishura},
journal= {arXiv preprint arXiv:1112.2330},
year = {2011}
}