Form of the Conditional Variance for Stable Random Variables

Renata Cioczek-Georges
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 .