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Form of the Conditional Variance for Stable Random
Murad S. Taqqu
Non-Gaussian stable random variables
always have infinite variance, but the
conditional second moment for a jointly -stable
vector with index
may exist when some
conditions on the spectral measure are met.
wu:cambanis:1991 obtained a functional form of the conditional
variance Var for symmetric -stable vectors with
. This paper extends their result to the whole range and also provides a formula for the conditional variance
in the case when are skewed and .