Some remarks on multivariate stable distributions

Abstract

This paper deals with multivariate stable distributions. Press has given an explicit algebraic representation of characteristic functions of such distributions [ J. Multivariate Analysis 2 (1972) , 444–462]. We present counter-examples and correct proofs of some of the statements of Press. The properties of multivariate stable distributions, connected with the spectral measure Γ, present in the expression of the characteristic function, are studied.