## Bernoulli

• Bernoulli
• Volume 13, Number 4 (2007), 1091-1123.

### Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation

#### Abstract

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence between the stable variables, some of which are new. The bounds are also used to deduce the central limit theorem for unbounded functions of stable moving average time series. This result extends the earlier results of Tailen Hsing and the authors on central limit theorems for bounded functions of stable moving averages. It can be used to show asymptotic normality of wavelet-based estimators of the self-similarity parameter in fractional stable motions.

#### Article information

Source
Bernoulli, Volume 13, Number 4 (2007), 1091-1123.

Dates
First available in Project Euclid: 9 November 2007

https://projecteuclid.org/euclid.bj/1194625604

Digital Object Identifier
doi:10.3150/07-BEJ6143

Mathematical Reviews number (MathSciNet)
MR2364228

Zentralblatt MATH identifier
1129.62021

#### Citation

Pipiras, Vladas; Taqqu, Murad S.; Abry, Patrice. Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation. Bernoulli 13 (2007), no. 4, 1091--1123. doi:10.3150/07-BEJ6143. https://projecteuclid.org/euclid.bj/1194625604

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