A Continuous Super-Brownian Motion in a Super-Brownian Medium

Donald A. Dawson () and Klaus Fleischmann ()

Journal of Theoretical Probability, 1997, vol. 10, issue 1, 213-276

Abstract: Abstract A continuous super-Brownian motion $$X^Q $$ is constructed in which branching occurs only in the presence of catalysts which evolve themselves as a continuous super-Brownian motion $$Q$$ . More precisely, the collision local time $$L_{[W,Q]}$$ (in the sense of Barlow et al. (1)) of an underlying Brownian motion path W with the catalytic mass process $$Q$$ goerns the branching (in the sense of Dynkin's additive functional approach). In the one-dimensional case, a new type of limit behavior is encountered: The total mass process converges to a limit without loss of expectation mass (persistence) and with a nonzero limiting variance, whereas starting with a Lebesgue measure $$\ell$$ , stochastic convergence to $$\ell$$ occurs.

Keywords: Catalytic reaction diffusion equation; catalyst process; random medium; catalytic medium; super-Brownian motion; superprocess; branching rate functional; measure-valued branching; critical branching; occupation time; jointly continuous occupation density; Hölder continuities; collision local time; persistence; super-Brownian medium (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1022606801625

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