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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 15, Fasc. ,
pages 195 - 214
 

CONDITIONAL VARIANCE FOR STABLE RANDOM VECTORS

Stamatis Cambanis
Stergios Fotopoulos

Abstract: For a symmetric a -stable random vector (X ,...,X ,X ) 1 n n+1 with 1 < a < 2 and spectral measure G, we find a necessary and sufficient condition in terms of G for the conditional variance V ar(X |X ,...,X ) n+1 1 n to be finite. We express the conditional variance in terms of G, and we develop an additivity property when X ,...,X 1 n are independent. These results are then applied to stable processes: scale mixtures of Gaussian processes, harmonizable and moving averages.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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