Decay Properties of Invariant Measure and Application to Elliptic Homogenization of Non-divergence Form with an Interface

Using the self-contained PDE analysis, this paper investigates the existence and the decay properties of the invariant measure in elliptic homogenization of non-divergence form with an interface assumptions on the leading coefficient $A$ and the drift $b$ for $b_1\equiv 0$, which partially provides an alternative proof of the previous work by Hairer and Manson [Ann. Probab. 39(2011) 648-682]. Moreover, as a direct application after using the analysis by the second author [Calc. Var. Partial Differ. Equ. 64(2025) No. 114], we obtain the quantitative estimates for the homogenization problem.