Central limit theorems for supercritical branching nonsymmetric Markov processes

• Yan-Xia Ren ^[1] ; Renming Song ^[2] ; Rui Zhang ^[1]
  1. [1] Peking University

     Peking University

     China

     
  2. [2] University of Illinois (Urbana-Champaign)
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 1, 2017, págs. 564-623
• Idioma: inglés
• DOI: 10.1214/14-AOP987
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• Resumen

  • 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.