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

Cénac P., Es-Sebaiy K.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 2

285--300

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 proces driven by fractional Brownian motion.