Subtree prune and regraft: A reversible real tree-valued Markov process

• 成果类型: Article
• 署名作者: Evans, Steven N.; Winter, Anita
• 署名单位: University of California System; University of California Berkeley; University of Erlangen Nuremberg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000034
• 发表日期: 2006
• 页码: 918-961
• 关键词: bessel-bridges; integration; SPACES; chain; parts; time

摘要

We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov-Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Dirichlet form hinges on a new path decomposition of the Brownian excursion.