Extinction properties of multi-type continuous-state branching processes
Extinction properties of multi-type continuous-state branching processes
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DOI：
10.1016/j.spa.2017.11.006
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发表时间：
2016-04
影响因子：
1.4
通讯作者：
A. Kyprianou;S. Palau
中科院分区：
文献类型：
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作者：
A. Kyprianou;S. Palau
最近在Barczy et al.（2015），引入了具有d型的多类型连续状态分支过程（具有移民）的概念作为d维向量值的解。在此之前，仿射过程的工作，最初的动机是数学金融，在Duffie等人。（2003）也证明了这种过程的存在。另见Gabrielli和Teichmann（2014）以及Caballero和Pérez Garmendia（2017）在这方面的最新贡献。关于多类型连续态分支过程的较早的工作更稀疏，但包括Watanabe（1969）和Ma（2013），其中只考虑了两种类型。在本文中，我们采取一种完全不同的方法，并考虑多类型的连续状态分支过程，现在允许一个可数无穷的类型，而不是定义为一个超马尔可夫链与本地和非本地分支机制。本着Engländer和Kypriano（2004）的精神，我们探索了它们的灭绝特性，并提出了一些开放的问题。
Recently in Barczy et al.(2015), the notion of a multi-type continuous-state branching process (with immigration) having d-types was introduced as a solution to an d-dimensional vector-valued SDE. Preceding that, work on affine processes, originally motivated by mathematical finance, in Duffie et al.(2003) also showed the existence of such processes. See also more recent contributions in this direction due to Gabrielli and Teichmann (2014) and Caballero and Pérez Garmendia (2017). Older work on multi-type continuous-state branching processes is more sparse but includes Watanabe (1969) and Ma (2013), where only two types are considered. In this paper we take a completely different approach and consider multi-type continuous-state branching process, now allowing for up to a countable infinity of types, defined instead as a super Markov chain with both local and non-local branching mechanisms. In the spirit of Engländer and Kypriano (2004) we explore their extinction properties and pose a number of open problems.