Open Access
2017 Exit laws of isotropic diffusions in random environment from large domains
Benjamin Fehrman
Electron. J. Probab. 22: 1-37 (2017). DOI: 10.1214/17-EJP79


This paper studies, in dimensions greater than two, stationary diffusion processes in random environment which are small, isotropic perturbations of Brownian motion satisfying a finite-range dependence. Such processes were first considered in the continuous setting by Sznitman and Zeitouni [21]. Building upon their work, it is shown by analyzing the associated elliptic boundary-value problem that, almost surely, the smoothed exit law of the diffusion from large domains converges, as the domain’s scale approaches infinity, to that of a Brownian motion. Furthermore, an algebraic rate for the convergence is established in terms of the modulus of the boundary condition.


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Benjamin Fehrman. "Exit laws of isotropic diffusions in random environment from large domains." Electron. J. Probab. 22 1 - 37, 2017.


Received: 26 September 2016; Accepted: 28 June 2017; Published: 2017
First available in Project Euclid: 10 August 2017

zbMATH: 1378.35022
MathSciNet: MR3690288
Digital Object Identifier: 10.1214/17-EJP79

Primary: 35B27 , 35J25 , 60H25 , 60J60 , 60K37

Keywords: Diffusion processes in random environment , Dirichlet boundary-value problem , Stochastic homogenization

Vol.22 • 2017
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