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Some properties of the range of super-Brownian motion
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  • Published: 01 July 1999

Some properties of the range of super-Brownian motion

  • Jean-François Delmas1 

Probability Theory and Related Fields volume 114, pages 505–547 (1999)Cite this article

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Abstract.

We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the ɛ-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X t is capacity-equivalent to [0, 1]2 in ℝd, d≥ 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1]4 in ℝd, d≥ 5.

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  1. MSRI, 1000 Centennial Drive, Berkeley, CA 94720, USA, USA

    Jean-François Delmas

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  1. Jean-François Delmas
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Received: 7 April 1998 / Revised version: 2 October 1998

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Delmas, JF. Some properties of the range of super-Brownian motion. Probab. Theory Relat. Fields 114, 505–547 (1999). https://doi.org/10.1007/s004400050233

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  • Published: 01 July 1999

  • Issue Date: July 1999

  • DOI: https://doi.org/10.1007/s004400050233

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  • Mathematics Subject Classification (1991): 60G57, 60J80
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