Factorization Property of Generalized s-self-decomposable measures and   class $L^f$ distributions
  The method of \emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will find such a representation for generalized s-selfdecomposable and selfdecomposable distributions that have the \emph{factorization property}. These are the classes $\mathcal{U}^f_{\be}$ and $L^f$, respectively. 
A. Czyzewska-Jankowska and Zbigniew J. Jurek
math.PR