# General Harris regularity criterion for non-linear Markov branching processes

Ramesh, N, Chen, A and Li, J
(2006)
*General Harris regularity criterion for non-linear Markov branching processes.*
Statistics & Probability Letters, 76.
pp. 446-452.
ISSN 0167-7152
(doi:10.1016/j.spl.2005.08.014)

## Abstract

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Item Type: | Article |
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Uncontrolled Keywords: | Markov branching process, non-linear Markov branching process, regularity |

Subjects: | Q Science > QA Mathematics |

School / Department / Research Groups: | School of Computing & Mathematical Sciences Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences > Department of Mathematical Sciences School of Computing & Mathematical Sciences > Statistics & Operational Research Group Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences > Statistics & Operational Research Group |

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Last Modified: | 31 Mar 2011 17:20 |

URI: | http://gala.gre.ac.uk/id/eprint/962 |

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