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.
|Title of host publication||Analytical methods in probability theory|
|Subtitle of host publication||proceedings of the conference held at Oberwolfach, Germany, June 9-14, 1980|
|Editors||D. Dugné, E. Lukacs, V.K. Rohatgi|
|Place of Publication||Berlin|
|Number of pages||5|
|Publication status||Published - 1981|
|Name||Lecture Notes in Mathematics|