Family size order statistics in branching processes with immigration

Authors: George P. Yanev ^a; Chris P. Tsokos ^a

Affiliation:

^a Department of Mathematics, University of South Florida, Tampa, FL, USA

DOI: 10.1080/07362990008809690

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 18, Issue 4 2000 , pages 655 - 670

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: PDF (English)

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Abstract

We study the kth largest value, ./LSAA_A_8809690_O_XML_IMAGES/LSAA_A_8809690_O_ILM0001.gif

, among the offspring of particles living in the (n-1)st generation of a branching process with immigration. In particular, ./LSAA_A_8809690_O_XML_IMAGES/LSAA_A_8809690_O_ILM0002.gif

./LSAA_A_8809690_O_XML_IMAGES/LSAA_A_8809690_O_ILM0002.gif

stands for the offspring of the most prolific particle in that generation. Limit theorems for ./LSAA_A_8809690_O_XML_IMAGES/LSAA_A_8809690_O_ILM0003.gif

./LSAA_A_8809690_O_XML_IMAGES/LSAA_A_8809690_O_ILM0003.gif

are proved. The results are obtained by combining extreme value theory methods and known results for the behavior of the population size in branching processes with immigration

Keywords: Branching Processes; Immigration; 60J80; 60G70; 60F05; Max-Stability; Order Statistics

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Family size order statistics in branching processes with immigration

Abstract