The Annals of Probability
- Ann. Probab.
- Volume 45, Number 1 (2017), 564-623.
Central limit theorems for supercritical branching nonsymmetric Markov processes
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.
Ann. Probab., Volume 45, Number 1 (2017), 564-623.
Received: April 2014
Revised: November 2014
First available in Project Euclid: 26 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
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