WIAS Preprint No. 261, (1996)

Longtime behavior of a branching process controlled by branching catalysts



Authors

  • Dawson, Donald A.
  • Fleischmann, Klaus

2010 Mathematics Subject Classification

  • 60J80 60J55 60G57

Keywords

  • catalytic reaction diffusion equation, super-Brownian motion, superprocess, branching functional, critical branching, measure-valued branching, persistence, super-Brownian medium, random medium, catalyst process, catalytic medium, Brownian collision local time, self-similarity, random ergodic limit

Abstract

The model under consideration is a catalytic branching model constructed in [DF96], where the catalysts themselves suffer a spatial branching mechanism. Main attention is paid to dimension d=3. The key result is a convergence theorem towards a limit with full intensity (persistence), which in a sense is comparable with the situation for the "classical" continuous super-Brownian motion. As by-products, strong laws of large numbers are derived for the Brownian collision local time controlling the branching of reactants, and for the catalytic occupation time process. Also, the occupation measures are shown to be absolutely continuous.

Appeared in

  • Stochastic Process. Appl., 71(2) (1997), pp. 241-257

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