Donnelly, Peter; Joyce, Paul Weak convergence of population genealogical processes to the coalescent with ages. (English) Zbl 0747.60034 Ann. Probab. 20, No. 1, 322-341 (1992). 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. Reviewer: E.I.Trofimov (Kazan’) Cited in 1 Document MSC: 60F99 Limit theorems in probability theory 60J75 Jump processes (MSC2010) 92D10 Genetics and epigenetics Keywords:genealogical processes; vector-valued function space of Skorokhod; weak convergence Citations:Zbl 0724.60040 PDFBibTeX XMLCite \textit{P. Donnelly} and \textit{P. Joyce}, Ann. Probab. 20, No. 1, 322--341 (1992; Zbl 0747.60034) Full Text: DOI