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Large deviations for Brownian motion in a random scenery
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  • Published: 18 June 2003

Large deviations for Brownian motion in a random scenery

  • Amine Asselah1 &
  • Fabienne Castell1 

Probability Theory and Related Fields volume 126, pages 497–527 (2003)Cite this article

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  • 18 Citations

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Abstract

We prove large deviations principles in large time, for the Brownian occupation time in random scenery \({{\frac{{1}}{{t}} \int_0^t \xi(B_s) \, ds}}\). The random field is constant on the elements of a partition of ℝd into unit cubes. These random constants, say \({{{{\left\lbrace{{ \xi(j), j \in \mathbb{{Z}}^d}}\right\rbrace}} }}\) consist of i.i.d. bounded variables, independent of the Brownian motion {B s ,s≥0}. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in ``quenched'' and ``annealed'' settings.

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Authors and Affiliations

  1. Laboratoire d'Analyse Topologie et Probabilités CNRS UMR 6632. CMI, Université de Provence, 39 rue Joliot Curie, 13453, Marseille Cedex 13, France

    Amine Asselah & Fabienne Castell

Authors
  1. Amine Asselah
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  2. Fabienne Castell
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Corresponding author

Correspondence to Amine Asselah.

Additional information

Mathematics Subject Classification (2000):60F10, 60J55, 60K37

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Cite this article

Asselah, A., Castell, F. Large deviations for Brownian motion in a random scenery. Probab. Theory Relat. Fields 126, 497–527 (2003). https://doi.org/10.1007/s00440-003-0265-3

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  • Received: 13 August 2002

  • Revised: 14 February 2003

  • Published: 18 June 2003

  • Issue Date: August 2003

  • DOI: https://doi.org/10.1007/s00440-003-0265-3

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Keywords

  • Random walk in random scenery
  • Large deviations
  • Additive functionals of Brownian motion
  • Random media
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