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This paper investigates quantitative estimates in elliptic homogenization ofnon-divergence form with unbounded drift and an interface, which continues thestudy of the previous work by Hairer and Manson [Ann. Probab. 39(2011)648-682], where they investigated the limiting long time/large scale behaviorof such a process under diffusive rescaling. We determine the effectiveequation and obtain the size estimates of the gradient of Green functions aswell as the optimal (in general) convergence rates. The proof relies ontransferring the non-divergence form into the divergence-form with thecoefficient matrix decaying exponentially to some (different) periodic matrixon the different sides of the interface first and then investigating thisspecial structure in homogenization of divergence form.

Quantitative Estimates in Elliptic Homogenization of Non-divergence Form with Unbounded Drift and an Interface