A calculus on Lévy exponents and selfdecomposability on Banach spaces

Details A calculus on Lévy exponents and selfdecomposability on Banach spaces A calculus on Lévy exponents and selfdecomposability on Banach spaces

2008-11-23

arxiv.org/abs/0811.3752v1

Probability and Mathematical Statistics, vol. 28 no 2, 2008, pp.271-280

Mathematics

Probability

11 pages

Scientific paper

In infinite dimensional Banach spaces there is no complete characterization of the L\'evy exponents of infinitely divisible probability measures. Here we propose \emph{a calculus on L\'evy exponents} that is derived from some random integrals. As a consequence we prove that \emph{each} selfdecomposable measure can by factorized as another selfdecomposable measure and its background driving measure that is s-selfdecomposable. This complements a result from the paper of Iksanov-Jurek-Schreiber in the Annals of Probability \textbf{32}, 2004.}

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