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Two limit theorems for critical Bellman-Harris branching processes. (English. Russian original) Zbl 0569.60084
Math. Notes 36, 546-550 (1984); translation from Mat. Zametki 36, No. 1, 109-116 (1984).
Let \(\mu_ t\) be the number of particles alive at time t in a critical Bellman-Harris process. Under conditions on regular variation of the tails of the offspring distribution and lifetime distribution it is shown that for \(c_ 1<...<c_ n\leq 1\) the conditional distribution of \((\mu_{c_ 1t},...,\mu_{c_ nt})\) given \(\mu_ t>0\) exists and may be identified with the corresponding finite-dimensional distribution in a certain Markov process. The case \(n=1\), \(c_ 1=c_ n=1\) was treated earlier by V. A. Vatutin, Teor. Veroyatn. Primen. 22, 150-155 (1977; Zbl 0391.60082).
Reviewer: S.Asmussen
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
Full Text: DOI
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