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Homogenization of a bond diffusion in a locally ergodic random environment

Olla, Stefano; Siri, Paola (2004), Homogenization of a bond diffusion in a locally ergodic random environment, Stochastic Processes and their Applications, 109, 2, p. 317-326. http://dx.doi.org/10.1016/j.spa.2003.10.009

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2002-37.pdf (209.1Kb)
Type
Article accepté pour publication ou publié
Date
2004
Journal name
Stochastic Processes and their Applications
Volume
109
Number
2
Publisher
Elsevier
Pages
317-326
Publication identifier
http://dx.doi.org/10.1016/j.spa.2003.10.009
Metadata
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Author(s)
Olla, Stefano cc
Siri, Paola
Abstract (EN)
We consider a nearest neighbors random walk on Image . The jump rate from site x to site x+1 is equal to the jump rate from x+1 to x and is a bounded, strictly positive random variable η(x). We assume that Image is distributed by a locally ergodic probability measure. We prove that, under diffusive scaling of space and time, the random walk converges in distribution to the diffusion process on Image with infinitesimal generator d/dX(a(X)d/dX), for a certain homogenized diffusion function a(X), independent of η. The main tools of the proof are a local ergodic result and the explicit solution of the corresponding Poisson equation.
Subjects / Keywords
Random walk in random environment; Homogenization; Invariance principle

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