Central limit theorems for supercritical branching nonsymmetric Markov processes

Yan Xia Ren, Renming Song, Rui Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)564-623
Number of pages60
JournalAnnals of Probability
Volume45
Issue number1
DOIs
StatePublished - Jan 1 2017

Keywords

  • Branching Markov process
  • Central limit theorem
  • Martingale
  • Supercritical

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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