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Conditional moments and linear regression for
stable random variables
Gennady Samorodnitsky
Murad S. Taqqu
Abstract:
Jointly -stable random variables with index
have only finite moments of order less than
, but their conditional moments can be higher than . We
provide conditions for this to happen and use the existence of the conditional
moments to study the regression . We show that if
is a symmetric -stable random vector, then under appropriate
conditions, the regression is well-defined even when and is
linear in x. The results are applied to different classes of symmetric
-stable processes.