Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein–Uhlenbeck processes

Abstrakt

We will investigate an almost sure central limit theorem ASCLT for sequences of random variables having the form of a ratio of two terms such that the numerator satisfies the ASCLT and the denominator is a positive term which converges almost surely to one. This result leads to the ASCLT for least squares estimators for Ornstein–Uhlenbeck process driven by fractional Brownian motion.