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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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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DOI: https://doi.org/10.1007/BF01200502
Mathematics Subject Classification
- 60G57
- 60G17