A Trotter-type approach to infinite rate mutually catalytic branching

Klenke, Achim; Oeler, Mario

Ann. Probab., Tome 38 (2010) no. 1, p. 479-497 / Harvested from Project Euclid

Résumé

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.

Publié le : 2010-03-15
Classification: Mutually catalytic branching, martingale problem, stochastic differential equations, population dynamics, Trotter formula, 60K35, 60K37, 60J80, 60J65, 60J35

@article{1268143524,
     author = {Klenke, Achim and Oeler, Mario},
     title = {A Trotter-type approach to infinite rate mutually catalytic branching},
     journal = {Ann. Probab.},
     volume = {38},
     number = {1},
     year = {2010},
     pages = { 479-497},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1268143524}
}

Klenke, Achim; Oeler, Mario. A Trotter-type approach to infinite rate mutually catalytic branching. Ann. Probab., Tome 38 (2010) no. 1, pp.  479-497. http://gdmltest.u-ga.fr/item/1268143524/