Electronic Resource
Springer
Probability theory and related fields
62 (1983), S. 147-163
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Self-decomposable probability measures μ on ℝ+ are characterized in terms of minus the logarithm of the Laplace transform of μ, say f, by the requirement that s→sf′(s) is again minus the logarithm of the Laplace transform of an infinitely divisible probability on ℝ+. Iteration of this condition yields characterizations in the case of ℝ+ of Urbanik's classes L n of multiply self-decomposable probabilities. The analogous characterization for discrete (multiply) self-decomposable probabilities on ℝ+ is discussed and used to give a representation of the generating functions for discrete completely self-decomposable probabilities on ℤ+. Classes of generalized Γ-convolutions analogous to the multiply self-decomposable probabilities on ℝ+ are studied as well as their discrete counterparts.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00538793
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