Large deviations and functional law for solutions of hyperbolic stochastic partial differential equations

Abstract

In this paper, we derive large deviation estimates of Freidlin–Wentzell for solutions of hyperbolic stochastic partial differential equation. This result generalizes those of Doss and Dozzi (1987), N’zi (1994) and Eddahbi (1997) to a large class of stochastic differential equations involving a two–parameter Wiener process. These solutions are obtained by small perturbations of the noise. As an application we give a functional law of the iterated logarithms.