CERTAIN PROBABILISTIC ASPECTS OF SEMISTABLE LAWS

MAKOTO MAEJIMA^{1} AND GENNADY SAMORODNITSKY^{2}

1Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan 2School of Operations Research and Industrial Engineering and

Department of Statistical Science, Cornell University, Ithaca, NY 14853, U.S.A.

(Received January 22, 1998; revised April 30, 1998)

Abstract. We study the extent to which the property of semistability of a random vector in ℜ^{d} is determined by semistability of its marginals, and the place of semistable laws within the family of type G and sub-stable laws. Similarities and differences between stable and semistable laws are discussed.

Key words and phrases: Semistable distribution, type G distribution, infinitely divisible distribution, stable distribution.