Norming constants for the finite mean supercritical Bellman-Harris process |
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Authors: | Harry Cohn |
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Affiliation: | (1) Dept. of Statistics R. Berry Bldg., University of Melbourne, 3052 Parkville, Victoria, Australia |
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Abstract: | Summary Let {Z(t)} be a supercritical Bellman-Harris process with offspring distribution {pk} and lifetime distributionG. It is shown that the finiteness of the offspring mean guarantees the existence of norming constants {C(t)} such that a.s. for some nondegenerate random variableW. C(t) is the -quantile of the distribution function ofZ(t), whereq< <1,q being the extinction probability of the process. As a byproduct of the proof, {Z(t)/C(t)} is shown to be asymptotic Markov. The theory of weakly stable sums of i.i.d. is used to get characterizations ofW and {C(t)}. |
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