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Approximation of exceedance processes in large populations. (English) Zbl 0986.60085

Consider a population of \(n\) individuals each of which generates a discrete-time stochastic branching process. The author studies the number of ancestors \(S(n,t)\) whose offspring at time \(t\) exceed a level \(\theta (t)\), where \(\theta (t)\) is a positive function. He describes conditions on the growth rate of \(\theta (t)\) and \(n=n(t)\) as \(t\to\infty\) under which \(S(n,t)\) converges in Skorokhod topology to stochastic processes with independent increments.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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