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MiS Preprint

Exit Laws of Isotropic Diffusions in Random Environment from Large Domains

Benjamin Fehrman


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 [20]. 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.

MSC Codes:
35B27, 35J25, 60H25, 60J60, 60K37
diffusion processes in random environment, stochastic homogenization, Dirichlet boundary-value problem

Related publications

2017 Journal Open Access
Benjamin J. Fehrman

Exit laws of isotropic diffusions in random environment from large domains

In: Electronic journal of probability, 22 (2017), p. 63