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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Mathematics Subject Classification (2000):60F10, 60J55, 60K37
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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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DOI: https://doi.org/10.1007/s00440-003-0265-3
Keywords
- Random walk in random scenery
- Large deviations
- Additive functionals of Brownian motion
- Random media