Electronic Journal of Probability

Exit laws of isotropic diffusions in random environment from large domains

Benjamin Fehrman

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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.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 63, 37 pp.

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

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Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 60K37: Processes in random environments 35J25: Boundary value problems for second-order elliptic equations 60H25: Random operators and equations [See also 47B80] 60J60: Diffusion processes [See also 58J65]

diffusion processes in random environment stochastic homogenization Dirichlet boundary-value problem

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Fehrman, Benjamin. Exit laws of isotropic diffusions in random environment from large domains. Electron. J. Probab. 22 (2017), paper no. 63, 37 pp. doi:10.1214/17-EJP79. https://projecteuclid.org/euclid.ejp/1502330523

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