ON THE CONVERGENCE RESULT FOR THE SUPERCRITICAL BELLMAN-HARRIS PROCESS1 |
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Authors: | Harry Cohn |
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Abstract: | It was proved in Cohn (1982) that for any finite offspring mean, supercritical Bellman-Harris process {Z(t)} there exist some norming constants {C(t)} such that {Z(t)/C(t)} converges almost surely to a non-degenerate random variable W. {C(t)} were defined to be the μ-quantiles of {Z(t)}. Schuh (1982) has given an alternative proof of this result, identifying C(t) as “the Seneta constants” 1/(-log Ft(-1)(γ)), where F1(γ) = E(γZ(t)). Both proofs are long and complicated. It will be shown here that a much simpler proof can be devised from Cohn (1982), if use is made of an elementarily proved property given in Schuh (1982). |
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