The Metric of Large Deviation Convergence

Tiefeng Jiang () and George L. O'Brien ()
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Tiefeng Jiang: Stanford University, Stanford
George L. O'Brien: York University

Journal of Theoretical Probability, 2000, vol. 13, issue 3, 805-824

Abstract: Abstract We construct a metric space of set functions ( $$Q\left( X \right)$$ , d) such that a sequence {P n} of Borel probability measures on a metric space ( $$X$$ , d*) satisfies the full Large Deviation Principle (LDP) with speed {a n} and good rate function I if and only if the sequence $$\left\{ {P_n^{a_n } } \right\}$$ converges in ( $$Q\left( X \right)$$ , d) to the set function e −I . Weak convergence of probability measures is another special case of convergence in ( $$Q\left( X \right)$$ , d). Properties related to the LDP and to weak convergence are then characterized in terms of ( $$Q\left( X \right)$$ , d).

Keywords: large deviations; metric spaces (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007814729591

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