The Metric of Large Deviation Convergence |
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| Authors: | Tiefeng Jiang George L. O'Brien |
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| Affiliation: | (1) Department of Statistics, Stanford University, Stanford, 370 Serra Mall, CA, 94305–4065;(2) Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada, M2N 3T5 |
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| Abstract: | We construct a metric space of set functions ( , d) such that a sequence {Pn} of Borel probability measures on a metric space ( , d*) satisfies the full Large Deviation Principle (LDP) with speed {an} and good rate function I if and only if the sequence  converges in ( , d) to the set function e–I. Weak convergence of probability measures is another special case of convergence in ( , d). Properties related to the LDP and to weak convergence are then characterized in terms of ( , d). |
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| Keywords: | large deviations metric spaces |
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