无限速率相互催化支化的Trotter型方法
A Trotter-type approach to infinite rate mutually catalytic branching
摘要：
道森和帕金斯[安。26（1988）1088 - 1138]建立了一个由可数位点空间索引的相互作用的两型种群的随机模型，该种群局部经历相互催化的分支机制。在Klenke和Mytnik [预印本（2008），arXiv：0901.0623]中，表明当分支速率接近无穷大时，该过程收敛于称为无穷大速率相互催化分支过程（IMUB）的过程。它最方便地被刻画为某个鞅问题的解。而在后者的参考文献中，噪声方程的方法是用来构造这个鞅问题的解决方案，本文的目的是提供一个Trotter型的建设。这里提出的结构将用于即将发表的论文，Klenke和Mytnik [预印本（2009）]，以研究IMUB的长期行为（类型的共存与分离）。本文部分是基于博士学位。第二作者的论文（2008年），其中首次介绍了特罗特方法。
英文摘要：
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.
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