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Extinction properties of multi-type continuous-state branching processes

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  • Kyprianou, Andreas E.
  • Palau, Sandra

Abstract

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.

Suggested Citation

  • Kyprianou, Andreas E. & Palau, Sandra, 2018. "Extinction properties of multi-type continuous-state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3466-3489.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:10:p:3466-3489
    DOI: 10.1016/j.spa.2017.11.006
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    References listed on IDEAS

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    1. Niemi, S. & Nummelin, E., 1986. "On non-singular renewal kernels with an application to a semigroup of transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 177-202, July.
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    Cited by:

    1. Dorottya Fekete & Sandra Palau & Juan Carlos Pardo & Jose Luis Pérez, 2021. "Backbone Decomposition of Multitype Superprocesses," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1149-1178, September.
    2. Shukai Chen, 2023. "On the Exponential Ergodicity of (2+2)-Affine Processes in Total Variation Distances," Journal of Theoretical Probability, Springer, vol. 36(1), pages 315-330, March.
    3. Palau, Sandra & Yang, Ting, 2020. "Law of large numbers for supercritical superprocesses with non-local branching," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1074-1102.

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