# Large deviations for Brownian motion in a random scenery

Research paper by A. Asselah, F. Castell

Indexed on: 13 Sep '02Published on: 13 Sep '02Published in: Mathematics - Probability

#### Abstract

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.