Stochastic Homogenization of Reflected Stochastic Differential Equations
Rhodes, Rémi (2010), Stochastic Homogenization of Reflected Stochastic Differential Equations, Electronic Journal of Probability, 15, Paper 31, p. 989-1023
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability
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Abstract (EN)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.
Subjects / Keywordslocal time; Skorohod problem; random medium; reﬂected stochastic differential equation; functional limit theorem; homogenization
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