Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes
Probability
2014-04-02 v1
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 \cite{RSZ2} 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.
Cite
@article{arxiv.1404.0116,
title = {Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes},
author = {Yan-Xia Ren and Renming Song and Rui Zhang},
journal= {arXiv preprint arXiv:1404.0116},
year = {2014}
}