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Weak convergence of population genealogical processes to the coalescent with ages. (English) Zbl 0747.60034

Finite size sample’s genealogical processes from an asymptotically infinite population are considered. Appropriately rescaled, they are shown to converge in distribution, in some \(\infty\)-dimensional vector- valued function space of Skorokhod. This proves former conjectures and includes the authors’ result [Adv. Appl. Probab. 23, No. 2, 229-258 (1991; Zbl 0724.60040)] on weak convergence of the equilibrium distributions of the processes.

MSC:

60F99 Limit theorems in probability theory
60J75 Jump processes (MSC2010)
92D10 Genetics and epigenetics

Citations:

Zbl 0724.60040
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