Homogenization of a bond diffusion in a locally ergodic random environment

Olla, Stefano; Siri, Paola

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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Type

Article accepté pour publication ou publié

Date

2004

Journal name

Stochastic Processes and their Applications

Volume

109

Number

Publisher

Elsevier

Pages

317-326

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