## The Annals of Probability

### Central limit theorems for supercritical branching nonsymmetric Markov processes

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 45, Number 1 (2017), 564-623.

Dates
Revised: November 2014
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.aop/1485421340

Digital Object Identifier
doi:10.1214/14-AOP987

Mathematical Reviews number (MathSciNet)
MR3601657

Zentralblatt MATH identifier
1365.60020

#### Citation

Ren, Yan-Xia; Song, Renming; Zhang, Rui. Central limit theorems for supercritical branching nonsymmetric Markov processes. Ann. Probab. 45 (2017), no. 1, 564--623. doi:10.1214/14-AOP987. https://projecteuclid.org/euclid.aop/1485421340

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