Convergence Rates and Limit Theorems for the Dual Markov Branching Process

Anthony G. Pakes

    Research output: Contribution to journal › Article

    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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    Markov Branching Process
    Limit Theorems
    Convergence Rate
    Optimal Rate of Convergence
    Specification

    Cite this

    Pakes, Anthony G. / Convergence Rates and Limit Theorems for the Dual Markov Branching Process. In: Journal of Probability and Statistics. 2017 ; Vol. 2017.
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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.",
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    Pakes, AG 2017, 'Convergence Rates and Limit Theorems for the Dual Markov Branching Process' Journal of Probability and Statistics, vol. 2017, 1410507. https://doi.org/10.1155/2017/1410507

    Convergence Rates and Limit Theorems for the Dual Markov Branching Process. / Pakes, Anthony G.

    In: Journal of Probability and Statistics, Vol. 2017, 1410507, 2017.

    Research output: Contribution to journal › Article

    TY - JOUR

    T1 - Convergence Rates and Limit Theorems for the Dual Markov Branching Process

    AU - Pakes, Anthony G.

    PY - 2017

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    N2 - 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.

    AB - 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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    U2 - 10.1155/2017/1410507

    DO - 10.1155/2017/1410507

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    JO - Journal of Probability and Statistics

    JF - Journal of Probability and Statistics

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    Pakes AG. Convergence Rates and Limit Theorems for the Dual Markov Branching Process. Journal of Probability and Statistics. 2017;2017. 1410507. https://doi.org/10.1155/2017/1410507

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