INFINITE RATE MUTUALLY CATALYTIC BRANCHING

• 成果类型: Article
• 署名作者: Klenke, Achim; Mytnik, Leonid
• 署名单位: Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP520
• 发表日期: 2010
• 页码: 1690-1716
• 关键词: brownian-motion; uniqueness

摘要

Consider the mutually catalytic branching process with finite branching rate gamma We show that as gamma -> infinity, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give descriptions of this process in terms of its semigroup in terms of the infinitesimal generator and as the solution of a martingale problem We also give a strong construction in terms of a planar Brownian motion from which we infer a path property of the process This is the first paper in a series or three, wherein we also construct an interacting version of this process and study its long-time behavior