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

Zhen Qing Chen; Yan Xia Ren; Ting Yang

doi:10.1007/s10959-016-0671-y

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

Zhen Qing Chen, Yan Xia Ren, Ting Yang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	898-931
Number of pages	34
Journal	Journal of Theoretical Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s10959-016-0671-y
Publication status	Published - 1 Sept 2017

Keywords

Branching Hunt processes
Law of large numbers
Spectral gap
Spine approach
h-transform

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10.1007/s10959-016-0671-y

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Chen, Z. Q., Ren, Y. X., & Yang, T. (2017). Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates. Journal of Theoretical Probability, 30(3), 898-931. https://doi.org/10.1007/s10959-016-0671-y

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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 Engl{\"a}nder et al. (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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N2 - 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.

AB - 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.

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KW - Law of large numbers

KW - Spectral gap

KW - Spine approach

KW - h-transform

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

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Keywords

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