Abstract
A function ϕ: [0, ∞)→(-∞,0] is the logarithm of the Laplace transform of an infinitely divisible probability measure on [0,∞) if and only if ϕ(0)=0, ϕ is continuous and conditionally positiv semi-definite.
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Literatur
FELLER, W.: An Introduction to Probability Theory and its Applications. Volume II. New York: Wiley 1966
GUICHARDET, A.: Symmetric Hilbert Spaces and Related Topics. Springer Lecture Notes, Bd. 261, Berlin 1972
JOHANSEN, S.: An Application of Extreme Point Methods to the Representation of Infinitely Divisible Distributions. Z. Wahrscheinlichkeitstheorie und verw. Gebiete S. 304–316, 1966
RESSEL, P.: Laplace-Transformation nichtnegativer und vektorwertiger Maße. manuscripta math. 13, 143–152, 1974.
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Ressel, P. Eine Charakterisierung unendlich oft teilbarer Verteilungen auf [0, ∞). Manuscripta Math 16, 47–49 (1975). https://doi.org/10.1007/BF01169062
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DOI: https://doi.org/10.1007/BF01169062