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A class of infinitely divisible distributions connected to branching processes and random walks
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
2004 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 295, no 1, 134-143 p.Article in journal (Refereed) Published
Abstract [en]

A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.

Place, publisher, year, edition, pages
Elsevier, 2004. Vol. 295, no 1, 134-143 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-7753DOI: 10.1016/j.jmaa.2004.03.018OAI: oai:DiVA.org:umu-7753DiVA: diva2:147424
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2014-03-19Bibliographically approved

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CiteExportLink to record
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