Self-decomposable discrete distributions and branching processes
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.
KeywordsNonnegative Integer Absolute Continuity Continuous Semigroup Probability Generate Function Divisible Distribution
Unable to display preview. Download preview PDF.
- Steutel, F.W., Vervaat, W. & Wolfe, S.J., Integer-valued branching processes with immigration. Forthcoming.Google Scholar