Abstract
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, Kotani’s lemma, allows us to compute the corresponding rate functions. The results are more explicit than in the discrete-time setting.
Citation
Marina Taleb. "Large Deviations for a Brownian Motion in a Drifted Brownian Potential." Ann. Probab. 29 (3) 1173 - 1204, July 2001. https://doi.org/10.1214/aop/1015345601
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