Abstract: I will discuss the problem of characterizing exit time and exit shape asymptotics from a domain of attraction for a stochastically perturbed partial differential equation (SPDE). This analysis requires proving that the sample paths of the SPDE satisfy certain large deviations principles that are uniform over bounded subsets of initial conditions (in a specified function space). Budhiraja, Dupuis, and Maroulas (2008) demonstrated that a weak-convergence approach can be used to prove uniform large deviations that are uniform over compact sets of initial conditions, but compact sets in infinite dimensional function spaces are too degenerate to be useful for these problems. I will discuss recent advances that allow us to use similar methods to prove uniform large deviations principles over (non-compact) bounded sets and in some cases we can prove uniformity over the entire function space.
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