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Law of large numbers for super-Brownian motions with a single point source

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  • Grummt, Robert
  • Kolb, Martin

Abstract

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimensions 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Suggested Citation

  • Grummt, Robert & Kolb, Martin, 2013. "Law of large numbers for super-Brownian motions with a single point source," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1183-1212.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1183-1212
    DOI: 10.1016/j.spa.2012.12.002
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    References listed on IDEAS

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    1. Engländer, János & Fleischmann, Klaus, 2000. "Extinction properties of super-Brownian motions with additional spatially dependent mass production," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 37-58, July.
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