Probability Theory and Related Fields

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

Thick points of super-Brownian motion

  • Jochen Blath
  • Peter Mörters


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.


Lower Bound Stochastic Process Probability Theory Mathematical Biology Hausdorff Dimension 
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© 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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