A NOTE ON CHARACTERIZATIONS OF MULTIVARIATE STABLE DISTRIBUTIONS

TRUC T. NGUYEN^{1} AND ALLAN R. SAMPSON^{2}

1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, U.S.A. 2Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

(Received December 5, 1989; revised May 23, 1990)

Abstract. Several characterizations of multivariate stable distributions together with a characterization of multivariate normal distributions and multivariate stable distributions with Cauchy marginals are given. These are related to some standard characterizations of Marcinkiewicz.

Key words and phrases: Multivariate stable distributions, Cauchy distribution, normal distribution, Marcinkiewicz theorem.