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

2015/02/28 by Zhen-Qing Chen, Chen, Zhen-Qing, Yan-Xia Ren +3
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1503.00106

openalex publication_date 2015/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Engländer-Harris-Kyprianou [Ann. Inst. Henri Poincaré 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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