Large Deviations of Solutions of Hyperbolic SPDE's in the Hölder Norm

Abstract

In this paper, we prove the large deviations principle for solutions of a hyperbolic stochastic partial differential equation, in the Holder topology of index α for all 0 ≤ α < \(\frac{1}{2}\). This result generalizes those in [5] and [10] to the Holder norm, and the result in [3] for solutions of a class fo stochastic differential equations involving a two-parameter Wiener process. These solutions are obtained by small perturbations of the noise.