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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

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Electronic Journal of Probability
Volume
15
Number
Paper 31
Pages
989-1023
Metadata
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Author(s)
Rhodes, Rémi
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 / Keywords
local time; Skorohod problem; random medium; reflected stochastic differential equation; functional limit theorem; homogenization