Abstract.
We determine for a super-Brownian motion {X t :t≥0} in ℝd, d≥3, the precise gauge function φ such that, almost surely on survival up to time t, 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.
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Acknowledgements. This work is part of the DFG project ‘‘Dimensionsspektren für die Super-Brownsche Bewegung’’ at Universität Kaiserslautern, and we would like to thank the Deutsche Forschungsgemeinschaft DFG for the support. We also thank the London Mathematical Society for a travel grant, which facilitated our collaboration. We owe thanks to an anonymous referee who pointed out substantial errors in a previous version of the paper. Last but not least we would like to thank David Hobson, Alison Etheridge and Heinrich von Weizsäcker for helpful discussions.
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Blath, J., Mörters, P. Thick points of super-Brownian motion. Probab. Theory Relat. Fields 131, 604–630 (2005). https://doi.org/10.1007/s00440-004-0387-2
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DOI: https://doi.org/10.1007/s00440-004-0387-2