WIAS Preprint No. 1154, (2006)

On the large scale behavior of super-Brownian motion in three dimensions with a single point source


  • Fleischmann, Klaus
  • Mueller, Carl
  • Vogt, Pascal

2010 Mathematics Subject Classification

  • 60J80 60K35


  • Super-Brownian motion with singular mass creation, expected mass, Schrödinger equation with one-point-potential


In a recent work, Fleischmann and Mueller (2004) showed the existence of a super-Brownian motion in R^d, d=2,3, with extra birth at the origin. Their construction made use of an analytical approach based on the fundamental solution of the heat equation with a one point potential worked out by Albeverio et al. (1995). The present note addresses two properties of this measure-valued process in the three-dimensional case, namely the scaling of the process and the large scale behavior of its mean.

Appeared in

  • Commun. Stoch. Anal., 1 (2007) pp. 19-28.

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