Large deviations for Brownian motion in a random scenery |
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Authors: | Amine Asselah Fabienne Castell |
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Affiliation: | (1) Laboratoire d'Analyse Topologie et Probabilités CNRS UMR 6632. CMI, Université de Provence, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France |
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Abstract: | We prove large deviations principles in large time, for the Brownian occupation time in random scenery . The random field is constant on the elements of a partition of d into unit cubes. These random constants, say consist of i.i.d. bounded variables, independent of the Brownian motion {Bs,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.Mathematics Subject Classification (2000):60F10, 60J55, 60K37 |
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Keywords: | Random walk in random scenery Large deviations Additive functionals of Brownian motion Random media |
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