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

  1. Peggy Cénac
  2. Khalifa Es-Sebaiy

Abstract

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 process driven by fractional Brownian motion.

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Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 285 to 300

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