Abstract
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-translation invariant problem making the usual method of the "environment as seen from the particle" inefficient.
Citation
Remi Rhodes. "Stochastic Homogenization of Reflected Stochastic Differential Equations." Electron. J. Probab. 15 989 - 1023, 2010. https://doi.org/10.1214/EJP.v15-776
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