Vol. 7, No. 8, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
Stochastic homogenization of viscous Hamilton–Jacobi equations and applications

Scott N. Armstrong and Hung V. Tran

Vol. 7 (2014), No. 8, 1969–2007

We present stochastic homogenization results for viscous Hamilton–Jacobi equations using a new argument that is based only on the subadditive structure of maximal subsolutions (i.e., solutions of the “metric problem”). This permits us to give qualitative homogenization results under very general hypotheses: in particular, we treat nonuniformly coercive Hamiltonians that satisfy instead a weaker averaging condition. As an application, we derive a general quenched large deviation principle for diffusions in random environments and with absorbing random potentials.

stochastic homogenization, Hamilton–Jacobi equation, quenched large deviation principle, diffusion in random environment, weak coercivity, degenerate diffusion
Mathematical Subject Classification 2010
Primary: 35B27
Received: 13 May 2014
Accepted: 7 October 2014
Published: 5 February 2015
Scott N. Armstrong
Centre de Recherche en Mathématiques de la Décision
Université Paris-Dauphine
Place du Maréchal de Lattre de Tassigny
75775 Paris 16
Hung V. Tran
Department of Mathematics
The University of Chicago
5734 South University Avenue
Chicago, IL 60637
United States