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Some dimension results for super-Brownian motion
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  • Published: September 1995

Some dimension results for super-Brownian motion

  • Laurent Serlet1 

Probability Theory and Related Fields volume 101, pages 371–391 (1995)Cite this article

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Summary

The Dawson-Watanabe super-Brownian motion has been intensively studied in the last few years. In particular, there has been much work concerning the Hausdorff dimension of certain remarkable sets related to super-Brownian motion. We contribute to this study in the following way. Let (Y t)t≧0 be a super-Brownian motion on ℝd(d≥2) andH be a Borel subset of ℝd. We determine the Hausdorff Dimension of {t≧0; SuppY t∩H≠Ø}, improving and generalizing a result of Krone. We also obtain a new proof of a result of Tribe which gives, whend≧4, the Hausdorff dimension of\( \cup _{t \in {\rm B}}\) SuppY t as a function of the dimension ofB.

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Authors and Affiliations

  1. Laboratoire de Probabilités Université Paris VI 4, Place Jussieu, F-75252, Paris Cedex 05, France

    Laurent Serlet

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  1. Laurent Serlet
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Serlet, L. Some dimension results for super-Brownian motion. Probab. Th. Rel. Fields 101, 371–391 (1995). https://doi.org/10.1007/BF01200502

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  • Received: 24 May 1994

  • Revised: 03 October 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01200502

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Mathematics Subject Classification

  • 60G57
  • 60G17
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