Elena Kosygina
CUNY
Title: Homogenization of Stochastic Hamilton-Jacobi-Bellman Equations.

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 the 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.

This is a joint work with F. Rezakhanlou (University of California, Berkeley) and S.R.S. Varadhan (Courant Institute, NYU).
©2006, Department of Mathematical Sciences
Last Modified: January 26, 2006