A TROTTER-TYPE APPROACH TO INFINITE RATE MUTUALLY CATALYTIC BRANCHING
成果类型：
Article
署名作者：
Klenke, Achim; Oeler, Mario
署名单位：
Johannes Gutenberg University of Mainz
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/09-AOP488
发表日期：
2010
页码：
479-497
关键词：
摘要：
Dawson and Perkins [Ann. Probab. 26 (1988) 1088-1138] constructed a stochastic model of an interacting two-type population indexed by a countable site space which locally undergoes a mutually catalytic branching mechanism. In Klenke and Mytnik [Preprint (2008), arXiv:0901.0623], it is shown that as the branching rate approaches infinity, the process converges to a process that is called the infinite rate mutually catalytic branching process (IMUB). It is most conveniently characterized as the solution of a certain martingale problem. While in the latter reference, a noise equation approach is used in order to construct a solution to this martingale problem, the aim of this paper is to provide a Trotter-type construction. The construction presented here will be used in a forthcoming paper, Klenke and Mytnik [Preprint (2009)], to investigate the long-time behavior of IMUB (coexistence versus segregation of types). This paper is partly based on the Ph.D. thesis of the second author (2008), where the Trotter approach was first introduced.