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

Access to Document

10.1007/BFb0097314

Fingerprint Dive into the research topics of 'Self-decomposable discrete distributions and branching processes'. Together they form a unique fingerprint.

Cite this

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

@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",

}

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

TY - CHAP

T1 - Self-decomposable discrete distributions and branching processes

AU - Harn, van, K.

AU - Steutel, F.W.

AU - Vervaat, W.

PY - 1981

Y1 - 1981

N2 - 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.

AB - 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.

U2 - 10.1007/BFb0097314

DO - 10.1007/BFb0097314

M3 - Chapter

SN - 978-3-540-10823-8

T3 - Lecture Notes in Mathematics

SP - 60

EP - 64

BT - Analytical methods in probability theory

A2 - Dugné, D.

A2 - Lukacs, E.

A2 - Rohatgi, V.K.

PB - Springer

CY - Berlin

ER -