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Markov branching processes with killing and resurrection

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Abstract

In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is honest and thus unique. We then further show that this honest Feller minimum process is not only positive recurrent but also strongly ergodic. The generating function of the important stationary distribution is explicitly expressed. For the interest of comparison and completeness, the results of the Markov branching processes with killing and instantaneous resurrection are also briefly stated. A new result regarding strong ergodicity of this difficult case is presented. The birth and death process with killing and resurrection together with another example is also analyzed.

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Authors and Affiliations

  1. Department of Financial Mathematics and Financial Engineering, South University of Science and Technology of China, Shenzhen, 518055, China

    AnYue Chen & Ying Lu

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK

    AnYue Chen

  3. Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China

    KaiWang Ng

  4. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    HanJun Zhang

Authors
  1. AnYue Chen
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  2. Ying Lu
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  3. KaiWang Ng
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  4. HanJun Zhang
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Correspondence to AnYue Chen.

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Chen, A., Lu, Y., Ng, K. et al. Markov branching processes with killing and resurrection. Sci. China Math. 59, 573–588 (2016). https://doi.org/10.1007/s11425-015-5069-2

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  • DOI: https://doi.org/10.1007/s11425-015-5069-2

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