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2010 Stochastic Homogenization of Reflected Stochastic Differential Equations
Remi Rhodes
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Electron. J. Probab. 15: 989-1023 (2010). DOI: 10.1214/EJP.v15-776

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.

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Remi Rhodes. "Stochastic Homogenization of Reflected Stochastic Differential Equations." Electron. J. Probab. 15 989 - 1023, 2010. https://doi.org/10.1214/EJP.v15-776

Information

Accepted: 28 June 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60049
MathSciNet: MR2659755
Digital Object Identifier: 10.1214/EJP.v15-776

Subjects:
Primary: 60F17
Secondary: 60K37, 74Q99

JOURNAL ARTICLE
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Vol.15 • 2010
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