Statistical inference for fractional diffusion process with random effects at discrete observations

Abstract

This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect parameters. First of all, we estimate the Hurst parameter H from one single subject. Second, assuming the Hurst index H is known, we derive the MLE and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects normally distributed.