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Regularly varying functions in the theory of simple branching processes

Published online by Cambridge University Press:  01 July 2016

E. Seneta
E. Seneta*
Affiliation:
Australian National University, Canberra
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Abstract

It is demonstrated for the non-critical and the explosive cases of the simple Bienaymé-Galton-Watson (B. G. W.) process (with and without immigration) that there exists a natural and intimate connection between regularly varying function theory and the asymptotic structure of the limit laws and corresponding norming constants. A similar fact had been demonstrated in connection with their invariant measures in [22]. This earlier study is complemented here by a similar analysis of the process where immigration occurs only at points of “emptiness” of the B. G. W. process.

Keywords

BIENAYMÉ-GALTON-WATSON PROCESSIMMIGRATIONLIMIT LAWSNORMING CONSTANTSREGULARLY VARYING FUNCTIONSINFINITE MEANINVARIANT MEASURES
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 3 , September 1974 , pp. 408 - 420
Copyright
Copyright © Applied Probability Trust 1974 

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