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Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

Published online by Cambridge University Press:  01 July 2016

H. Hering
H. Hering*
Affiliation:
Universität Regensburg
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Abstract

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

Keywords

BRANCHING-IMMIGRATION PROCESSARBITRARY SET OF TYPESDISCRETE OR CONTINUOUS PARAMETERINHOMOGENEOUS POISSON IMMIGRATIONHOMOGENEOUS MARKOV BRANCHING PARTSUPERCRITICAL BRANCHING PARTNORMALIZED AVERAGING PROCESSESMEAN SQUARE CONVERGENCEALMOST SURE CONVERGENCE OF SKELETONSALMOST SURE CONVERGENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 468 - 494
Copyright
Copyright © Applied Probability Trust 1975 

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