Abstract
An Ornstein-Uhlenbeck process in a periodic potential inR dis considered. It has been shown previously that this process satisfies a central limit theorem in the sense that, by rescaling space and time in a suitable way, the distribution of the process converges to that of a Wiener process with nonsingular diffusion matrix. Here a rigorous proof is given of a version of Einstein's formula for this model, relating the diffusion constant to the “mobility” of the system.
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Rodenhausen, H. Einstein's relation between diffusion constant and mobility for a diffusion model. J Stat Phys 55, 1065–1088 (1989). https://doi.org/10.1007/BF01041079
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DOI: https://doi.org/10.1007/BF01041079