Let (X1, X2) be a symmetric [alpha]-stable random vector with 0 [alpha] 2. Its distribution is characterized by a finite measure [GH] on the unit circle called the spectral measure. It is known that if [GH] satisfies some integrability condition then the conditional moment E[X2pX1 = x] can...

C. D. Hardin, Jr., G. Samorodnitsky, and M. S. Taqqu (1991,Ann. Appl. Probab. 1 582-612) have shown that the regression E[Y X = x] is typically asymptotically linear when (X, Y) is an [alpha]-stable random vector with [alpha] 2. We provide necessary and sufficient conditions for asymptotic...

Let (X1,X2) be an [alpha]-stable random vector with 0 [alpha] 2, not necessarily symmetric. Its distribution is characterized by a finite measure [Gamma] on the unit circle called the spectral measure. It is known that if [Gamma] satisfies some integrability condition then the conditional...