MULTITYPE A-COALESCENTS

• 成果类型: Article
• 署名作者: Johnston, Samuel G. G.; Kyprianou, Andreas; Rogers, Tim
• 署名单位: University of London; King's College London; University of Warwick; University of Bath
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1891
• 发表日期: 2023
• 页码: 4210-4237
• 关键词: mergers

摘要

Consider a multitype coalescent process in which each block has a colour in {1, ... , d}. Individual blocks may change colour, and some number of blocks of various colours may merge to form a new block of some colour. We show that if the law of a multitype coalescent process is invariant under permutations of blocks of the same colour, has consistent Markovian projec-tions, and has asynchronous mergers, then it is a multitype A-coalescent: a process in which single blocks may change colour, two blocks of like colour may merge to form a single block of that colour, or large mergers across vari-ous colours happen at rates governed by a d-tuple of measures on [0, 1]d. We go on to identify when such processes come down from infinity. Our frame-work generalises Pitman's celebrated classification theorem for singletype coalescent processes, and provides a unifying setting for numerous examples that have appeared in the literature, including the seed-bank model, the island model, and the coalescent structure of continuous-state branching processes.