Extinction properties of multi-type continuous-state branching processes
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Publication:1615898
DOI10.1016/J.SPA.2017.11.006zbMATH Open1409.60127arXiv1604.04129OpenAlexW2963678859MaRDI QIDQ1615898
Author name not available (Why is that?)
Publication date: 31 October 2018
Published in: (Search for Journal in Brave)
Abstract: Recently in Barczy, Li and Pap (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 math- ematical finance, in Duffie, Filipovic and Schachermayer (2003) also showed the existence of such processes. See also more recent contributions in this direction due to Gabrielli and Teichmann (2014) and Caballero, Perez Garmendia and Uribe Bravo (2015). 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 Englander and Kyprianou (2004) we explore their extinction properties and pose a number of open problems.
Full work available at URL: https://arxiv.org/abs/1604.04129
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