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New Limiting Distributions for Bellman-Harris Processes

Part of: Markov processes Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Wolfgang P. Angerer
Wolfgang P. Angerer*
Affiliation:
Texas A&M University
*
∗Current address: Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, km 2.5 Carretera a Acatlima, Huajuapan de León, Oaxaca CP 69000, México. Email address: [email protected]
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Abstract

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We present a number of new solutions to an integral equation arising in the limiting theory of Bellman-Harris processes. The argument proceeds via straightforward analysis of Mellin transforms. We also derive a criterion for the analyticity of the Laplace transform of the limiting distribution on Re(u) ≥ -c for some c > 0.

Keywords

Mellin transformbranching processexponential moment

MSC classification

Secondary: 44A05: General transforms 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 313 - 321
Copyright
Copyright © Applied Probability Trust 2011 

References

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