We consider a nearest neighbors random walk on Z. 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 eta(x). We assume that {eta(x)} with x∈Z 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 R with infinitesimal generator d/dX(a(X)d/dX), for a certain homogenized diffusion function a(X), independent of eta . The main tools of the proof are a local ergodic result and the explicit solution of the corresponding Poisson equation.
Homogenization of a bond diffusion in a locally ergodic random environment / Olla, S.; Siri, Paola. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 109:(2004), pp. 317-326.
Homogenization of a bond diffusion in a locally ergodic random environment
SIRI, PAOLA
2004
Abstract
We consider a nearest neighbors random walk on Z. 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 eta(x). We assume that {eta(x)} with x∈Z 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 R with infinitesimal generator d/dX(a(X)d/dX), for a certain homogenized diffusion function a(X), independent of eta . The main tools of the proof are a local ergodic result and the explicit solution of the corresponding Poisson equation.Pubblicazioni consigliate
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https://hdl.handle.net/11583/1950110
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