Almost sure central limit theorems for random ratios and applications to   LSE for fractional Ornstein-Uhlenbeck processes
  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. 
Peggy C\'enac and Khalifa Es-Sebaiy
math.PR