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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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2017/1410507 |
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| _version_ | 1849690437157126144 |
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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. |
| format | Article |
| id | doaj-art-eb66521c141f4e49989463ea669d9092 |
| institution | DOAJ |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |