Abstract
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 language | English (US) |
---|---|
Pages (from-to) | 805-824 |
Number of pages | 20 |
Journal | Journal of Theoretical Probability |
Volume | 13 |
Issue number | 3 |
DOIs | |
State | Published - 2000 |
Bibliographical note
Funding Information:1Department of Statistics, 370 Serra Mall, Stanford University, Stanford, CA 94305-4065. E-mail: tjiang stat.stanford.edu. 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 yorku.ca. Research of this author supported in part by the Natural Sciences and Engineering Research Council of Canada.
Keywords
- Large deviations
- Metric spaces