Abstract
In infinite dimensional Banach spaces there is no complete characterization of the Lévy exponents of infinitely divisible probability measures. Here we propose \emph{a calculus on Lévy 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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