Decomposition of Supercritical Linear-Fractional Branching Processes

• 作者: Altynay Shaimerdenova Serik Sagitov
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Harris-Sevastyanov Transformation Dual REPRODUCTION Law Branching PROCESS with Countably Many Types MULTIVARIATE Linear-Fractional Distribution Bienaymé-Galton-Watson PROCESS Conditioned Branching PROCESS
• 年，卷（期）: 2013,（2）
• 页码范围: 352-359
• 页数: 8页
• 分类号: O1

摘要

It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.