Let ℱ denote the convolution semigroup of probability distributions on the real line. We prove that no element of ℱ is prime in the sense that given an ℱ one can always find two distributions G,H∈ℱ such that F is a convolution factor of G*H but neither of G nor of H. In contrast, ℱ is known to possess many irreducible elements.
|Number of pages||7|
|Journal||Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete|
|Publication status||Published - Aug 1 1985|
ASJC Scopus subject areas
- Statistics and Probability