Large deviations for Brownian motion in a random scenery

Details Large deviations for Brownian motion in a random scenery Large deviations for Brownian motion in a random scenery

2002-09-13

arxiv.org/abs/math/0209160v1

Mathematics

Probability

29 pages

Scientific paper

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. 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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