Abstract
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.
Citation
Nils Caillerie. Julien Vovelle. "Diffusion-approximation for a kinetic equation with perturbed velocity redistribution process." Ann. Appl. Probab. 31 (3) 1299 - 1335, June 2021. https://doi.org/10.1214/20-AAP1619
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