Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

Zhen-Qing Chen (), Yan-Xia Ren () and Ting Yang ()
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Zhen-Qing Chen: University of Washington
Yan-Xia Ren: Peking University
Ting Yang: Beijing Institute of Technology

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 898-931

Abstract: Abstract We establish weak and strong laws 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 the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374–399, 2007) and for branching diffusions by Engländer et al. (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.

Keywords: Law of large numbers; Branching Hunt processes; Spine approach; h-transform; Spectral gap; Primary 60J25; Secondary 60J80 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-016-0671-y

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