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June, 1976 An Age-Dependent Model with Parental Survival
Thomas H. Savits
Ann. Probab. 4(3): 382-392 (June, 1976). DOI: 10.1214/aop/1176996087


We consider an age-dependent model which not only allows the generating function to be age-dependent, but also allows the parent to reproduce several times during its lifetime. By using the notion of $\vee$-space-time harmonic functions, we study the behavior of $Z_t$, the number of particles alive at time $t$, in the supercritical case. In particular we obtain results which are analogous to the classically known results for the Bellman-Harris model; in fact, we obtain convergence in probability.


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Thomas H. Savits. "An Age-Dependent Model with Parental Survival." Ann. Probab. 4 (3) 382 - 392, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0356.60049
MathSciNet: MR402961
Digital Object Identifier: 10.1214/aop/1176996087

Primary: 60J80

Keywords: Age-dependent process , convergence in law , Harmonic function , parental survival , space-time martingale

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
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