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We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

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Abstract:We develop homogenization results of a degenerate semilinear PDE with a Wentzell-type boundary condition. The second order operator is also degenerate. Our approach is entirely probabilistic, and extends the result of Diakhaby and Ouknine [3].