Central limit theorems for supercritical branching nonsymmetric Markov processes

Yan Xia Ren, Renming Song, Rui Zhang

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - 2017


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Central limit theorems for supercritical branching nonsymmetric Markov processes'. Together they form a unique fingerprint.

Cite this