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January 2017 Central limit theorems for supercritical branching nonsymmetric Markov processes
Yan-Xia Ren, Renming Song, Rui Zhang
Ann. Probab. 45(1): 564-623 (January 2017). DOI: 10.1214/14-AOP987


In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in Ren, Song and Zhang [J. Funct. Anal. 266 (2014) 1716–1756] for supercritical branching symmetric Markov processes. To prove our central limit theorem, we have to carefully develop the spectral theory of nonsymmetric strongly continuous semigroups, which should be of independent interest.


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Yan-Xia Ren. Renming Song. Rui Zhang. "Central limit theorems for supercritical branching nonsymmetric Markov processes." Ann. Probab. 45 (1) 564 - 623, January 2017.


Received: 1 April 2014; Revised: 1 November 2014; Published: January 2017
First available in Project Euclid: 26 January 2017

zbMATH: 1365.60020
MathSciNet: MR3601657
Digital Object Identifier: 10.1214/14-AOP987

Primary: 60F05 , 60J80
Secondary: 60J25 , 60J35

Keywords: Branching Markov process , central limit theorem , martingale , supercritical

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 1 • January 2017
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