文章基本信息

标题：On hitting probabilities of beta coalescents and absorption times of coalescents that come down from infinity
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作者：Martin Möhle
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2014
卷号：XI
页码：141-159
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Let X = (Xk)k=0;1;::: denote the jump chain of the block countingprocess of the -coalescent with = (2 􀀀 ; ) being the beta distribution withparameter 2 (0; 2). A solution for the hitting probability h(n;m) that the chainX ever visits the state m, conditional that it starts in the state X0 = n, is obtainedvia an analytic method based on generating functions. For 2 (1; 2) the results areapplied to characterize the distribution of the almost sure limit of the absorptiontimes n of the coalescent restricted to a sample of size n. The latter result isgeneralized to arbitrary exchangeable coalescents (-coalescents) that come downfrom innity. The results generalize those obtained for the particular case = 1in Mohle, M. (2014) Asymptotic hitting probabilities for the Bolthausen{Sznitmancoalescent, J. Appl. Probab. 51A, to appear. This article furthermore supplementsthe work of Henard, O. (2013), The xation line, Preprint, arXiv:1307.0784.
关键词：Absorption time; beta coalescent; Bolthausen{Sznitman coalescent;coming down from innity; generating functions; Green matrix; hitting probability.