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In this article, we obtain a functional CLT for a class of degeneratediffusion processes with periodic coefficients, thus generalizing the alreadyclassical results in the context of uniformly elliptic diffusions. As anapplication, we also discuss periodic homogenization of a class of lineardegenerate elliptic and parabolic PDEs.

A CLT for degenerate diffusions with periodic coefficients, and application to homogenisation of linear PDEs