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A super-Brownian motion with a locally infinite catalytic mass
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  • Published: 01 October 2002

A super-Brownian motion with a locally infinite catalytic mass

  • Klaus Fleischmann1 &
  • Carl Mueller2 

Probability Theory and Related Fields volume 107, pages 325–357 (1997)Cite this article

  • 65 Accesses

  • 8 Citations

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Summary.

A super-Brownian motion \(X\) in \({\Bbb R}\) with “hyperbolic” branching rate \(\varrho _2(b)=1/b^2\), \(\;b\in {\Bbb R},\,\) is constructed, which symbolically could be described by the formal stochastic equation \({\rm d}X_t\,=\,\textstyle \frac 12\,\Delta X_t\,{\rm d}t+\sqrt{2\varrho _2X_t}\,{\rm d}W_{t\,},\qquad t>0, \label{stochequ}\) (with a space-time white noise \({\rm d}W\)). Starting at \(X_0=\delta _{a\,},\) \(\,a\ne 0,\) this superprocess \(X\) will never hit the catalytic center: There is an increasing sequence of Brownian stopping times \(\tau _n\) strictly smaller than the hitting time of \(\,0\) such that with probability one Dynkin's stopped measures \(X_{\tau _n}\) vanish except for finitely many \(n.\)

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany (e-mail: fleischmann@wias-berlin.de), Berlin, Germany

    Klaus Fleischmann

  2. Department of Mathematics, University of Rochester, Rochester, NY 14620, USA (e-mail: cmlr@troi.rochester.edu), Rochester, NY, USA

    Carl Mueller

Authors
  1. Klaus Fleischmann
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  2. Carl Mueller
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Received: 27 November 1995 / In revised form: 24 July 1996

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Fleischmann, K., Mueller, C. A super-Brownian motion with a locally infinite catalytic mass. Probab Theory Relat Fields 107, 325–357 (1997). https://doi.org/10.1007/s004400050088

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  • Published: 01 October 2002

  • Issue Date: March 1997

  • DOI: https://doi.org/10.1007/s004400050088

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  • Mathematics Subject Classification (1991): Primary 60J80; Secondary 60J55, 60G57
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