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arXiv · 1112.2330

On drift parameter estimation in models with fractional Brownian motion

Yuriy Kozachenko·Alexander Melnikov·Yuliya Mishura
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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.

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Yuriy Kozachenko, Alexander Melnikov, Yuliya Mishura. 2011-12-11. On drift parameter estimation in models with fractional Brownian motion. https://arxiv.org/abs/1112.2330

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