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Large Deviations for a Brownian Motion in a Drifted Brownian Potential

Large Deviations for a Brownian Motion in a Drifted Brownian Potential

We derive a large deviation principle both quenched and annealed for a one-dimensional diffusion process in a drifted Brownian environment providing the continuous time analogue of what Comets, Gantert and Zeitouni recently establish for the random walk in random environment. A key-ingredient, Kotaniā€™s lemma, allows us to compute the corresponding ā€¦