Some properties of the range of super-Brownian motion |
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Authors: | Jean-François Delmas |
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Affiliation: | (1) MSRI, 1000 Centennial Drive, Berkeley, CA 94720, USA, US;(2) ENPC-CERMICS, 6 av. Blaise Pascal, Champs-sur-Marne, F-77455 Marne La Vallée, France. e-mail: delmas@enpc.cermics.fr, FR |
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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. Received: 7 April 1998 / Revised version: 2 October 1998 |
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Keywords: | Mathematics Subject Classification (1991): 60G57 60J80 |
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