Extinction properties of multi-type continuous-state branching processes |
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Authors: | Andreas E Kyprianou Sandra Palau |
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Institution: | Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK |
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Abstract: | Recently in Barczy et al. (2015), the notion of a multi-type continuous-state branching process (with immigration) having -types was introduced as a solution to an -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. |
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Keywords: | 60G99 60J68 60J80 Continuous-state branching process Superprocess Multi-type process Local extinction |
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