The Metric of Large Deviation Convergence

Tiefeng Jiang, George L. O'Brien

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We construct a metric space of set functions (script Q sign(script X sign), d) such that a sequence {Pn} of Borel probability measures on a metric space (script X sign, d*) satisfies the full Large Deviation Principle (LDP) with speed {an} and good rate function I if and only if the sequence {Pann} converges in (script Q sign(script X sign), d) to the set function e-I. Weak convergence of probability measures is another special case of convergence in (script Q sign(script X sign), d). Properties related to the LDP and to weak convergence are then characterized in terms of (script Q sign(script X sign), d).

Original languageEnglish (US)
Pages (from-to)805-824
Number of pages20
JournalJournal of Theoretical Probability
Issue number3
StatePublished - 2000

Bibliographical note

Funding Information:
1Department of Statistics, 370 Serra Mall, Stanford University, Stanford, CA 94305-4065. E-mail: tjiang Present address: School of Statistics, 313 Ford Hall, 224 Church Street S.E., Minneapolis, MN 55455. 2Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M2N 3T5. E-mail: obrien Research of this author supported in part by the Natural Sciences and Engineering Research Council of Canada.


  • Large deviations
  • Metric spaces


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