Convergence Rates and Limit Theorems for the Dual Markov Branching Process

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    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.

    Original languageEnglish
    Article number1410507
    JournalJournal of Probability and Statistics
    Volume2017
    DOIs
    Publication statusPublished - 2017

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