Moments of random vectors which belong to some domain of normal attraction (Q918560)

Under the assumption that the distribution of a k-dimensional random vector X belongs to the domain of normal attraction of some operator stable law \(\nu\), it is shown that the sets of \(\alpha\) for which E \(| <X,\theta >|^{\alpha}\) exists depend on both \(\theta\) and \(\nu\), and a complete description of these sets is given.