Rate of convergence in the law of large numbers for supercritical general multi-type branching processes
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Publication:2512853
DOI10.1016/J.SPA.2014.10.004zbMATH Open1327.60061arXiv1401.1368OpenAlexW2050125471MaRDI QIDQ2512853
Author name not available (Why is that?)
Publication date: 30 January 2015
Published in: (Search for Journal in Brave)
Abstract: We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded single-type process composed of all individuals having the same type as the ancestor. As an important intermediate step, we determine the (exact) polynomial rate of convergence of Nerman's martingale in continuous time to its limit. The techniques used also allow us to give streamlined proofs of the weak and strong laws of large numbers and ratio convergence for the processes in focus.
Full work available at URL: https://arxiv.org/abs/1401.1368
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