@inbook{806e179ebc8242e99959ca5102dd8a31,

title = "Self-decomposable discrete distributions and branching processes",

abstract = "Self-decomposable distributions are known to be absolutely continuous. In this note analogues of the concept of self-decomposability are proposed for distributions on the set ℕ0 of nonnegative integers. To each of them corresponds an analogue of multiplication (in distribution) that preserves ℕ0-valuedness and is characterized by a composition semigroup of probability generating functions, such as occur in branching processes.",

author = "{Harn, van}, K. and F.W. Steutel and W. Vervaat",

year = "1981",

doi = "10.1007/BFb0097314",

language = "English",

isbn = "978-3-540-10823-8",

series = "Lecture Notes in Mathematics",

publisher = "Springer",

pages = "60--64",

editor = "D. Dugn{\'e} and E. Lukacs and V.K. Rohatgi",

booktitle = "Analytical methods in probability theory",

address = "Germany",

}