MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Exit Laws of Isotropic Diffusions in Random Environment from Large Domains
Benjamin FehrmanAbstract
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.
- Received:
- 08.07.16
- Published:
- 15.07.16
- MSC Codes:
- 35B27, 35J25, 60H25, 60J60, 60K37
- Keywords:
- diffusion processes in random environment, stochastic homogenization, Dirichlet boundary-value problem