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

Rüdiger Murr

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1729-1749

Abstract: 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.

Keywords: Duality formula; Integration by parts formula; Malliavin calculus; Infinite divisibility; Lévy processes; Random measures (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2012.12.012

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