(Received November 8, 1995; revised May 13, 1996)
Abstract. Klebanov et al. (1985, Theory Probab. Appl., 29, 791-794) introduced a class of probability laws termed by them ``geometrically-infinitely-divisible'' laws, and studied in detail the sub-class of ``geometrically-strictly-stable'' laws. In Section 2 of the present paper, the larger sub-class of ``geometric-stable'' laws is (defined and) studied. In Section 3, a characterization of stable processes involving (stochastic integrals and) geometric-stable laws is presented. In Section 4, the asymptotic behaviour of stable densities of exponent one (and |beta| < 1) is studied using only real analysis methods. In an Appendix, ``geometric domains of attraction'' to geometric-stable laws are investigated, motivated by the work of Mohan et al. (1993, Sankhyã Ser. A, 55, 171-179).
Key words and phrases: Stable laws and processes, geometric-stable laws, geometric domains of attraction.
Source ( TeX , DVI , PS )