Title: Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations,
Abstract: We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener
process and a spectrally positive strictly stable Lévy process, and we study
asymptotic properties of the maximum likelihood estimator (MLE) for its growth
rate based on continuous time observations. We distinguish three cases:
subcritical, critical and supercritical. In all cases we prove strong
consistency of the MLE in question, in the subcritical case asymptotic
normality, and in the supercritical case asymptotic mixed normality are shown
as well. In the critical case the description of the asymptotic behavior of the
MLE in question remains open.