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 Electronic Journal of Probability > Vol. 15(2010) > Paper 31 open journal systems 


Stochastic Homogenization of Reflected Stochastic Differential Equations

Remi Rhodes, Université Paris-Dauphine, Ceremade


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.


Full text: PDF

Pages: 989-1023

Published on: June 28, 2010
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Electronic Journal of Probability. ISSN: 1083-6489