  We study the homogenization problem for a system of stochastic differential
equation with local time terms that models a multivariate diffusion in presence
of semipermeable hyperplane interfaces with oblique penetration. We show that
this system has a unique weak solution and determine its weak limit as the
distances between the interfaces converge to zero. In the limit, the singular
local times terms vanish and give rise to an additional regular
interface-induced drift.

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