%0 Journal Article
%T A calculus on L¨¦vy exponents and selfdecomposability on Banach spaces
%A Zbigniew J. Jurek
%J Mathematics
%D 2008
%I arXiv
%X 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.}
%U http://arxiv.org/abs/0811.3752v1