Non parametric estimation for fractional diffusion processes with random effects

ABSTRACT

We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random effects and non-random diffusion. We build ordinary kernel estimators and histogram estimators and study their $L^p$risk ($p=1\text{or}2$), when $H>1/2$. Asymptotic results are evaluated as both $T=T\left(N\right)$ and N tend to infinity.

KEYWORDS:

• Random effects model
• fractional Brownian motion
• nonparametric estimation
• density estimator
• histogram estimator

AMS SUBJECT CLASSIFICATIONS:

• 62G86
• 60G22
• 62G20

Acknowledgements

We would like to thank the editorial staff and the referees for the comments that helped in improving this work. Also, we would like to thank the supporter of this work: The the Germano-Morrocan Program for Scientific Research PMARS 2015-060.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hamid El Maroufy http://orcid.org/0000-0001-6113-7543