Abstract
We apply the theory developed in Part I to study diffusions with generators with stationary and ergodic coefficients that are uniformly elliptic and can be written in a divergence form. The approach is similar to the one used in Chap. 3 for the random walk in random environment and in Chap. 5 for the tagged particle: the trajectory of a particle can be written as a sum of an additive functional of the environment seen from the particle, and a martingale. The generator of the environment process satisfies the sector condition and the central limit theorem for the trajectory is a direct consequence of the results from Chap. 2. We discuss the connection to the analytical results of the homogenization of diffusion equations with periodic coefficients, as a particular case of the general ergodic case.
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Komorowski, T., Landim, C., Olla, S. (2012). Diffusions in Random Environments. In: Fluctuations in Markov Processes. Grundlehren der mathematischen Wissenschaften, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29880-6_9
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DOI: https://doi.org/10.1007/978-3-642-29880-6_9
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