Convergence Rates and Limit Theorems for the Dual Markov Branching Process

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 branchin...

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Main Author: Anthony G. Pakes
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2017/1410507
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author Anthony G. Pakes
author_facet Anthony G. Pakes
author_sort Anthony G. Pakes
collection DOAJ
description 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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issn 1687-952X
1687-9538
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publishDate 2017-01-01
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series Journal of Probability and Statistics
spelling doaj-art-eb66521c141f4e49989463ea669d90922025-08-20T03:21:18ZengWileyJournal of Probability and Statistics1687-952X1687-95382017-01-01201710.1155/2017/14105071410507Convergence Rates and Limit Theorems for the Dual Markov Branching ProcessAnthony G. Pakes0School of Mathematics & Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, AustraliaThis 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.http://dx.doi.org/10.1155/2017/1410507
spellingShingle Anthony G. Pakes
Convergence Rates and Limit Theorems for the Dual Markov Branching Process
Journal of Probability and Statistics
title Convergence Rates and Limit Theorems for the Dual Markov Branching Process
title_full Convergence Rates and Limit Theorems for the Dual Markov Branching Process
title_fullStr Convergence Rates and Limit Theorems for the Dual Markov Branching Process
title_full_unstemmed Convergence Rates and Limit Theorems for the Dual Markov Branching Process
title_short Convergence Rates and Limit Theorems for the Dual Markov Branching Process
title_sort convergence rates and limit theorems for the dual markov branching process
url http://dx.doi.org/10.1155/2017/1410507
work_keys_str_mv AT anthonygpakes convergenceratesandlimittheoremsforthedualmarkovbranchingprocess