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High Level Occupation Times for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
Published online by Cambridge University Press: 20 November 2018
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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 l < ∞ the set {x:I(x) ≦ l} is a compact set in X.
(iv) For each closed set C ⊂ X
(v) For each open set C ⊂ X
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- Copyright © Canadian Mathematical Society 1987