On characterization of multivariate stable distributions via random linear statistics
A random linear statistic \(U\) is a linear combination of \(n\) nondegenerate, independent and identically distributed \(d\times 1\) random vectors \(X_ i\), \(i=1,\dots, n\), when the coefficients form an \(n\times 1\) random vector \(Y\) independent of the \(X_ i\)'s. Multivariate strictly stable distributions of \(X_ 1\) are characterized through independence of \(U\) and \(Y\), when \(Y\) satisfies certain conditions. Some choices of \(Y\) satisfying the stated conditions are given. Characterizations through identical distributions of \(U\) and \(X_ 1\) are also discussed. Specific examples are given for the case \(n=2\).
scientific article; zbMATH DE number 727270
scientific article