Stochastic Homogenization of Reflected Diffusion Processes

Details Stochastic Homogenization of Reflected Diffusion Processes Stochastic Homogenization of Reflected Diffusion Processes

2007-12-20

arxiv.org/abs/0712.3416v3

Mathematics

Probability

29 pages

Scientific paper

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.

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