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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

Anna T. Lawniczak
Anna T. Lawniczak*
Affiliation:
University of Toronto, Toronto, Ontario
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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

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 239 - 256
Copyright
Copyright © Canadian Mathematical Society 1987

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