Elena Kosygina: On the connection between large deviations of diffusions in random environments and homogenization of some stochastic Hamilton-Jacobi-Bellman (HJB) equations

This is a tutorial talk, no knowledge of large deviations is assumed. I shall explain the large deviations problem on a simple example, introduce a large deviation principle, and then show that homogenization of a certain class of HJB equations is equivalent to the large deviations principle for quenched path measures of diffusions in random environment. This connection brings some probabilistic intuition and techniques into the homogenization problem.