Higher Order Asymptotics for Large Deviations (Pratima Hebbar - University of Maryland)

For sequences of weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth Expansions for the Central Limit Theorem. Motivated by studying branching diffusion processes in periodic media, we obtain such expansions for additive functionals of processes generated from Stochastic Differential Equations satisfying the Hörmander condition on a compact manifold. This is joint work with Kasun Fernando.