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

Peggy Cénac; Khalifa Es-Sebaiy

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arXiv · 1209.0137

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

Peggy Cénac·Khalifa Es-Sebaiy

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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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Peggy Cénac, Khalifa Es-Sebaiy. 2012-09-01. Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes. https://arxiv.org/abs/1209.0137

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