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A note on the Lévy-Khinchin representation of negative definite functions on Hilbert spaces

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

Gunter Ritter
Gunter Ritter
Affiliation:
Fakultät für Mathematik und InformatikUniversität PassauD-8390 Passau, West Germany
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Abstract

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We study negative definite functions on a Hilbert space and use their properties to give a proof of the Lévy-Khinchin formula for an infinitely divisible probability distribution on .

Keywords

Lévy-Khinchin representationnegative definite functionsgenerating functionssemigroups of probability distributionsHilbert spaces.

MSC classification

Secondary: 60E07: Infinitely divisible distributions; stable distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 104 - 116
Copyright
Copyright © Australian Mathematical Society 1988

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