Sharp large deviation estimates for the stochastic heat equation

We consider the family {X-epsilon, epsilon greater than or equal to0} of so lution to the heat equation on [0,T]x[0,1] perturbed by a small space-time white noise, that is partial derivative X-t(epsilon)=partial derivative (x) ,x(2)X(epsilon)+b({X-epsilon})+epsilon sigma({X-epsilon})(W) over dot. Then , for a large class of Borelian subsets of the continuous functions on [0,T ]x[0,1], we get an asymptotic expansion of P(X epsilon is an element ofA) a s epsilon SE arrow0. This kind of expansion has been handled for several st ochastic systems, ranging from Wiener integrals to diffusion processes.