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Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments. (English. French summary) Zbl 1246.35029
The authors deal with the (stochastic) homogenization of Hamilton-Jacobi equations and Bellman equations posed in stationary, ergodic, unbounded media. They obtain in the limit deterministic Hamilton-Jacobi equations and study the properties of the effective Hamiltonian. It seems that the class of problems studied here is motivated by the work of A.-S. Sznitman [Brownian motion, obstacles and random media. Berlin: Springer (1993; Zbl 0973.60003)] on quenched large deviations of the Brownian motion interacting with a Poisson-like potential.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60K37 Processes in random environments
35F21 Hamilton-Jacobi equations
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