Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures

Processes with independent increments are proven to be the unique solutions of duality formulas. This result is based on a simple characterization of infinitely divisible random vectors by a functional equation in which a difference operator appears. This operator is constructed by a variational method and compared to approaches involving chaos decompositions. We also obtain a related characterization of infinitely divisible random measures.

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Year of publication:	2013
Authors:	Murr, Rüdiger
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 5, p. 1729-1749
Publisher:	Elsevier
Subject:	Duality formula \| Integration by parts formula \| Malliavin calculus \| Infinite divisibility \| Lévy processes \| Random measures

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011065009