Homogenization of a bond diffusion in a locally ergodic random environment

S. Olla and P. Siri

Stochastic Processes and their Applications, 2004, vol. 109, issue 2, 317-326

Abstract: We consider a nearest neighbors random walk on . 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 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 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.

Keywords: Random; walk; in; random; environment; Homogenization; Invariance; principle (search for similar items in EconPapers)
Date: 2004
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