CENTRAL LIMIT THEOREMS FOR SUPERCRITICAL BRANCHING NONSYMMETRIC MARKOV PROCESSES

• 成果类型: Article
• 署名作者: Ren, Yan-Xia; Song, Renming; Zhang, Rui
• 署名单位: Peking University; Peking University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP987
• 发表日期: 2017
• 页码: 564-623
• 关键词: Diffusions

摘要

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.