Large Deviation Principle for White Noise Gaussian Measures

In the theory of large deviations, one of the main result is the Schilder's theorem. It gives the large deviation estimates for a family {μ_∈,∈ > 0} of measures on some Polish space X, which tends weakly to the Dirac measure δ_p at the point p ∈ X. In this paper, we investigate analogous problems for a family {γ_∈,∈ > 0} of white noise Gaussian measures with mean 0 and variance ∈ on the Schwartz distributions space S′(ℝ).