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Journal of Probability and Statistics
Volume 2017 (2017), Article ID 1410507, 13 pages
https://doi.org/10.1155/2017/1410507
Research Article

Convergence Rates and Limit Theorems for the Dual Markov Branching Process

School of Mathematics & Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

Correspondence should be addressed to Anthony G. Pakes; ua.ude.awu@sekap.ynot

Received 15 July 2016; Accepted 23 February 2017; Published 16 March 2017

Academic Editor: Ramón M. Rodríguez-Dagnino

Copyright © 2017 Anthony G. Pakes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.