Statistical inference for discretely observed fractional diffusion processes with random effects

Abstract

We address statistical inference for linear fractional diffusion processes with random effects in the drift. In particular, we investigate maximum likelihood estimators (MLEs) of the random effect parameters. First of all, we estimate the Hurst parameter

H\in (0,1)

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from one single subject. Second, assuming that the Hurst index

H\in (0,1)

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H\in (0,1)$$\end{document}

is known, we derive the MLEs and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects being normally distributed.

Keywords

Asymptotic normality / Fractional Brownian motion / Long-range memory process / Random effects model / Strong consistency / Mathematical Sciences / Statistics

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Funding

Morocco-German Scientific program(PMARS III 2015/060)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature