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Convergence Rates and Limit Theorems for the Dual Markov Branching Process

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  • Anthony G. Pakes

Abstract

This paper studies aspects of the Siegmund dual of the Markov branching process. The principal results are optimal convergence rates of its transition function and limit theorems in the case that it is not positive recurrent. Additional discussion is given about specifications of the Markov branching process and its dual. The dualising Markov branching processes need not be regular or even conservative.

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  • Anthony G. Pakes, 2017. "Convergence Rates and Limit Theorems for the Dual Markov Branching Process," Journal of Probability and Statistics, Hindawi, vol. 2017, pages 1-13, March.
    • Handle: RePEc:hin:jnljps:1410507
    DOI: 10.1155/2017/1410507
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    Cited by:

    1. Foucart, Clément & Möhle, Martin, 2022. "Asymptotic behaviour of ancestral lineages in subcritical continuous-state branching populations," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 510-531.

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