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Stone-Weierstrass type theorems for large deviations


 
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1. Title Title of document Stone-Weierstrass type theorems for large deviations
 
2. Creator Author's name, affiliation, country Henri Comman; University of Santiago de Chile
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large deviations, rate function, Bryc's theorem
 
3. Subject Subject classification 60F10
 
4. Description Abstract We give a general version of Bryc's theorem valid on any topological space and with any algebra $\mathcal{A}$ of real-valued continuous functions separating the points, or any well-separating class. In absence of exponential tightness, and when the underlying space is locally compact regular and $\mathcal{A}$ constituted by functions vanishing at infinity, we give a sufficient condition on the functional $\Lambda(\cdot)_{\mid \mathcal{A}}$ to get large deviations with not necessarily tight rate function. We obtain the general variational form of any rate function on a completely regular space; when either exponential tightness holds or the space is locally compact Hausdorff, we get it in terms of any algebra as above. Prohorov-type theorems are generalized to any space, and when it is locally compact regular the exponential tightness can be replaced by a (strictly weaker) condition on $\Lambda(\cdot)_{\mid \mathcal{A}}$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Research supported by DICYT-USACH grant No. 040533C
 
7. Date (YYYY-MM-DD) 2008-04-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1370
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1370
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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