A Critical Branching Process with Stationary-Limiting Distribution

Authors: George P. Yanev ^a^b; Nickolay M. Yanev ^c

Affiliations:	^a University of South Florida St. Petersburg, St. Petersburg, Florida, USA
	^b University of South Florida St. Petersburg, St. Petersburg, FL, USA
	^c Bulgarian Academy of Sciences, Sofia, Bulgaria

DOI: 10.1081/SAP-120030453

Publication Frequency: 6 issues per year

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Stochastic Analysis and Applications, Volume 22, Issue 3 January 2005 , pages 721 - 738

Subjects: Statistics & Probability; Stochastic Models & Processes;

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Abstract

Seneta (Seneta, E. The stationary distribution of a branching process allowing immigration: A remark on the critical case. J. Royal Statistical Society, Series B 1968, 30, 176-179) shows that a critical branching process with pure immigration has a stationary-limiting distribution provided that its offspring variance is infinite. We obtain a stationary-limiting distribution keeping the variance finite but allowing an emigration-immigration component in each generation.

Keywords: Critical branching processes; Emigration; Immigration; Stationary and quasi-stationary distribution

1991 AMS Subject Classification: 60J80

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A Critical Branching Process with Stationary-Limiting Distribution

Abstract