On positive distributions of the class \(L\) of self-decompsable laws. (English. Ukrainian original) Zbl 0998.60014

Iksanov, O. M.

Theory Probab. Math. Stat. 64, 51-61 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 48-56 (2001).

The author discusses properties of distributions from a special subclass \(L^{*}\) of positive infinite divisible Linnik laws which are regularly varying in a neighborhood of zero. Various equivalent definitions and characterizations of the class \(L^{*}\) are presented. In particular, the Mittag-Leffler distributions are investigated.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60E05	Probability distributions: general theory
33E12	Mittag-Leffler functions and generalizations
60E07	Infinitely divisible distributions; stable distributions

Keywords:

selfdecomposable distributions; infinitely divisible distributions; Poisson process; Linnik distributions; Mittag-Leffler distributions; characterization