WIAS Preprint No. 546, (2000)

Catalytic and mutually catalytic super-Brownian motions


Authors

  • Dawson, Donald A.
  • Fleischmann, Klaus

2010 Mathematics Subject Classification

  • 60K35 60G57 60J80

Keywords

  • Mutually catalytic branching, catalytic super-random walk, catalyst, reactant, superprocess, measure-valued branching, absolute continuity, collision measure, collision local time, self-similarity, martingale problem, segregation of types, coexistence of types, self-duality, finite time extinction, ultimate extinction, biodiversity, cyclic reaction

DOI

10.20347/WIAS.PREPRINT.546

Abstract

Catalytic branching processes describe the evolution of two types of material (populations) called catalyst and reactant. The catalyst evolves autonomously, but catalyzes the reactant. The individuals of both populations share the features of motion, growth and death. In mutually catalytic models however there is an additional feedback from the reactant to the catalyst destroying completely the basic independence assumption of branching theory. Recent results for continuum models of this type are surveyed.

Appeared in

  • Seminar on Stochastic Analysis, Random Fields and Applications III, Centro Stefano Franscini, Ascona, Switzerland, September 19-24, 1999, R. C. Dalang, M. Dozzi,, F. Russo, (eds.), vol. 52 of Progress in Probability, Birkhaeuser-Verlag, Basel, 2002, pp. 89-110

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