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Thick points of super-Brownian motion
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  • Published: 12 September 2004

Thick points of super-Brownian motion

  • Jochen Blath1 &
  • Peter Mörters2 

Probability Theory and Related Fields volume 131, pages 604–630 (2005)Cite this article

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  • 2 Citations

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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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Authors and Affiliations

  1. Department of Statistics, University of Oxford, 1, South Parks Road, Oxford, OX1 3TG, UK

    Jochen Blath

  2. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    Peter Mörters

Authors
  1. Jochen Blath
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  2. Peter Mörters
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Corresponding author

Correspondence to Jochen Blath.

Additional information

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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Cite this article

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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  • Received: 02 February 2004

  • Revised: 19 May 2004

  • Published: 12 September 2004

  • Issue Date: April 2005

  • DOI: https://doi.org/10.1007/s00440-004-0387-2

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Keywords

  • Lower Bound
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Hausdorff Dimension
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