Almost sure central limit theorems for random ratios and applications to lse for fractional ornstein–uhlenbeck processes

2012

We investigate an almost sure 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 1. This result leads to the ASCLT for least square estimators for Ornstein-Uhlenbeck process driven by fractional Brownian motion.