Large deviations for stochastic Volterra equations in the plane

We prove a Large Deviation Principle for the family of solutions of Volterr a equations in the plane obtained by perturbation of the driving white nois e. One of the motivations for the study of such class of equations is provi ded by non-linear hyperbolic stochastic partial differential equations appe aring in the construction of some path-valued processes on manifolds. The p roof uses the method developped by Azencott for diffusion processes. The ma in ingredients are exponential inequalities for different classes of two-pa rameter stochastic integrals; these integrals are related to the representa tion of the stochastic term in the differential equation as a representable semimatringale.