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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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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DOI: https://doi.org/10.1007/s004400050233
- Mathematics Subject Classification (1991): 60G57, 60J80