Self-decomposable discrete distributions and branching processes

K. Harn, van; F.W. Steutel; W. Vervaat

doi:10.1007/BFb0097314

Self-decomposable discrete distributions and branching processes

K. Harn, van, F.W. Steutel, W. Vervaat

Mathematics and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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.

Original language	English
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
Publisher	Springer
Pages	60-64
Number of pages	5
ISBN (Electronic)	978-3-540-36785-7
ISBN (Print)	978-3-540-10823-8
DOIs	https://doi.org/10.1007/BFb0097314
Publication status	Published - 1981

Publication series

Name	Lecture Notes in Mathematics
Volume	861
ISSN (Print)	0075-8434

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10.1007/BFb0097314

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Harn, van, K., Steutel, F. W., & Vervaat, W. (1981). Self-decomposable discrete distributions and branching processes. In D. Dugné, E. Lukacs, & V. K. Rohatgi (Eds.), Analytical methods in probability theory: proceedings of the conference held at Oberwolfach, Germany, June 9-14, 1980 (pp. 60-64). (Lecture Notes in Mathematics; Vol. 861). Springer. https://doi.org/10.1007/BFb0097314

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Harn, van, K, Steutel, FW & Vervaat, W 1981, Self-decomposable discrete distributions and branching processes. in D Dugné, E Lukacs & VK Rohatgi (eds), Analytical methods in probability theory: proceedings of the conference held at Oberwolfach, Germany, June 9-14, 1980. Lecture Notes in Mathematics, vol. 861, Springer, Berlin, pp. 60-64. https://doi.org/10.1007/BFb0097314

Self-decomposable discrete distributions and branching processes. / Harn, van, K.; Steutel, F.W.; Vervaat, W.

Analytical methods in probability theory: proceedings of the conference held at Oberwolfach, Germany, June 9-14, 1980. ed. / D. Dugné; E. Lukacs; V.K. Rohatgi. Berlin : Springer, 1981. p. 60-64 (Lecture Notes in Mathematics; Vol. 861).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Self-decomposable discrete distributions and branching processes

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