Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces

Abstract

Let X be a complete, separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I( · ) if there exists a function I( · ) from X into [0, ∞] satisfying:(i) 0 ≦ I(x) ≦ ∞ for all x ∊ X,(ii) I( · ) is lower semicontinuous,(iii) for each 1 < ∞ the set {x:I(x) ≦ 1} is compact set in X,(iv) for each closed set C ⊂ X(v) for each open set U ⊂ XIt is easy to see that if A is a Borel set such thatthenwhere A0 and Ā are respectively the interior and the closure of the Borel set A.