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Probability Theory and Related Fields

, Volume 131, Issue 4, pp 604–630 | Cite as

Thick points of super-Brownian motion

  • Jochen Blath
  • Peter Mörters
Article

Abstract.

We determine for a super-Brownian motion {X t :t≥0} in ℝ d , d≥3, the precise gauge function φ such that, almost surely on survival up to time t, Open image in new window improving a result of Barlow, Evans and Perkins about the most visited sites of super-Brownian motion. We also determine upper and lower bounds for the Hausdorff dimension spectrum of thick points refining the multifractal analysis of super-Brownian motion by Taylor and Perkins. The upper bound, conjectured to be sharp, involves a constant which can be characterized in terms of the upper tails of the associated equilibrium Palm distribution.

Keywords

Lower Bound Stochastic Process Probability Theory Mathematical Biology Hausdorff Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of OxfordOxfordUK
  2. 2.Department of Mathematical SciencesUniversity of BathBathUK

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