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arXiv · 1503.00106

Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates

Zhen-Qing Chen·Yan-Xia Ren·Ting Yang
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Abstract

We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state-dependent. Our work is motivated by recent work on strong law of large numbers for branching symmetric Markov processes by Chen-Shiozawa [J. Funct. Anal., 250, 374--399, 2007] and for branching diffusions by Engl\"ander-Harris-Kyprianou [Ann. Inst. Henri Poincar\'e Probab. Stat., 46, 279--298, 2010]. Our results can be applied to some interesting examples that are covered by neither of these papers.

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Zhen-Qing Chen, Yan-Xia Ren, Ting Yang. 2015-02-28. Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates. https://arxiv.org/abs/1503.00106

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