WIAS Preprint No. 706, (2001)

Mass-time-space scaling of a super-Brownian catalyst reactant pair


Authors

  • Fleischmann, Klaus
  • Xiong, Jie

2010 Mathematics Subject Classification

  • 60K35 60G57 60J80

Keywords

  • Catalyst, reactant, superprocess, martingale problem, stochastic equation, density field, collision measure, colision local time, extinction, critical scaling

DOI

10.20347/WIAS.PREPRINT.706

Abstract

The one-dimensional super-Brownian reactant Xϱ with a super-Brownian catalyst ϱ has a jointly continuous density field satisfying a stochastic partial differential equation. Consider any expectation preserving mass-time-space scaling of Xϱ. Using the density field, one can pass to an fdd scaling limit of the measure-valued process, which degenerates also under the critical scaling of ϱ. For some of the scaling indexes, convergence on path spaces holds, too.

Appeared in

  • J. Theoret. Probab., 19 (2006) pp. 557-588.

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