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

2012/09/01 by Peggy Cénac, Cénac, Peggy, Khalifa Es-Sebaiy +1
Mathematics · #60F05 #60G15 #60H05 #60H07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05 #msc:60G15 #msc:60H05 #msc:60H07

paper · pdf · doi:10.48550/arxiv.1209.0137

arxiv created 2012/09/01 · arxiv updated 2012/09/04

Abstract

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.

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