## IMA Postdoc Seminar (December 01, 2009)

**Speaker:** Maroulas, Vasileios (IMA)

**Title: **Variational representations, small noise large deviations and applications.

**Abstract: **Variational representations for infinite dimensional Brownian motions and Poisson random measures are considered in order to establish small noise (uniform) large deviations. Using this approach, a large deviation principle for a class of stochastic reaction-diffusion equations is established under conditions that are substantially weaker than those available in the literature, and large deviation estimates for a family of infinite dimensional stochastic flows of diffeomorphisms that arise in certain image analysis problems are demonstrated. The small noise large deviations results for the stochastic diffeomorphic flows are then applied to a stochastic Bayesian formulation of an image matching problem, and an approximate maximum likelihood property is shown for the solution of an optimization problem involving the large deviations rate function. This talk is based on joint works with A. Budhiraja and P. Dupuis.