Stochastic homogenization of Hamilton-Jacobi-Bellman equations

Elena Kosygina, Fraydoun Rezakhanlou, S. R S Varadhan

Research output: Contribution to journalArticlepeer-review

Abstract

We study the homogenization of some Hamilton-Jacobi-Bellman equations with a vanishing second-order term in a stationary ergodic random medium under the hyperbolic scaling of time and space. Imposing certain convexity, growth, and regularity assumptions on the Hamiltonian, we show the locally uniform convergence of solutions of such equations to the solution of a deterministic "effective" first-order Hamilton-Jacobi equation. The effective Hamiltonian is obtained from the original stochastic Hamiltonian by a minimax formula. Our homogenization results have a large-deviations interpretation for a diffusion in a random environment.

Original languageEnglish (US)
Pages (from-to)1489-1521
Number of pages33
JournalCommunications on Pure and Applied Mathematics
Volume59
Issue number10
DOIs
StatePublished - Oct 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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