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We study a kinetic toy model for a spray of particles immersed in an ambientfluid, subject to some additional random forcing given by a mixing,space-dependent Markov process. Using the perturbed test function method, wederive the hydrodynamic limit of the kinetic system. The law of the limitingdensity satisfies a stochastic conservation equation in Stratonovich form,whose drift and diffusion coefficients are completely determined by the law ofthe stationary process associated with the Markovian perturbation.

Diffusion-approximation for a kinetic spray-like system with random forcing