A TROTTER-TYPE APPROACH TO INFINITE RATE MUTUALLY CATALYTIC BRANCHING

作者：Klenke Achim^*; Oeler Mario

来源：Annals of Probability, 2010, 38(2): 479-497.

DOI：10.1214/09-AOP488

• Mutually catalytic branching
• martingale problem
• stochastic differential equations
• population dynamics
• Trotter formula

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.

• 出版日期2010-3