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Longtime behavior of a branching process controlled by branching catalysts

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  • Dawson, Donald A.
  • Fleischmann, Klaus

Abstract

The model under consideration is a catalytic branching model constructed in Dawson and Fleischmann (1997), where the catalysts themselves undergo a spatial branching mechanism. The key result is a convergence theorem in dimension d = 3 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 catalytic occupation measures are shown to be absolutely continuous with respect to Lebesgue measure. © 1997 Elsevier Science B.V.

Suggested Citation

  • Dawson, Donald A. & Fleischmann, Klaus, 1997. "Longtime behavior of a branching process controlled by branching catalysts," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 241-257, November.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:2:p:241-257
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    References listed on IDEAS

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    1. Dawson, Donald A. & Fleischmann, Klaus, 1988. "Strong clumping of critical space-time branching models in subcritical dimensions," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 193-208, December.
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    Cited by:

    1. Klenke, Achim, 2000. "Absolute continuity of catalytic measure-valued branching processes," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 227-237, October.
    2. Greven, A. & Klenke, A. & Wakolbinger, A., 2002. "Interacting diffusions in a random medium: comparison and longtime behavior," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 23-41, March.
    3. Pinsky, Ross G., 2003. "Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 117-137, May.

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