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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 35, Fasc. 2,
pages 285 - 300
 

ALMOST SURE CENTRAL LIMIT THEOREMS FOR RANDOM RATIOS AND APPLICATIONS TO LSE FOR FRACTIONAL ORNSTEIN–UHLENBECK PROCESSES

Peggy Cénac
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.

2000 AMS Mathematics Subject Classification: Primary: 60F05, 60G15, 60H05, 60H07; Secondary: 62F12.

Keywords and phrases: Almost sure central limit theorem, least squares estimator, fractional Ornstein–Uhlenbeck process, multiple stochastic integrals.

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