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We establish bounds for the covariance of a large class of functions ofinfinite variance stable random variables, including unbounded functions suchas the power function and the logarithm. These bounds involve measures ofdependence between the stable variables, some of which are new. The bounds arealso used to deduce the central limit theorem for unbounded functions of stablemoving average time series. This result extends the earlier results of TailenHsing and the authors on central limit theorems for bounded functions of stablemoving averages. It can be used to show asymptotic normality of wavelet-basedestimators of the self-similarity parameter in fractional stable motions.

bernoulli

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