Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-30T05:02:28.146Z Has data issue: false hasContentIssue false
  • English
  • Français

On large deviations of empirical measures in the τ-topology

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

A. De Acosta
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

Keywords

LARGE DEVIATIONSEMPIRICAL MEASURESSANOV'S THEOREMτ -TOPOLOGY

MSC classification

Primary: 60F10: Large deviations
Type
Part 2 Probabilistic Methods
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 41 - 47
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] De Acosta, A. (1985) On large deviations of sums of independent random vectors. Lecture Notes in Mathematics 1153, 1–14, Springer-Verlag, Berlin.Google Scholar
[2] De Acosta, A. (1990) Large deviations for empirical measures of Markov chains. J. Theoret. Prob. 3, 395–431.CrossRefGoogle Scholar
[3] Azencott, R. (1980) Grandes déviations et applications. Lectures Notes in Mathematics 774, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Bahadur, R. R. and Zabell, S. (1979) Large deviations of the sample mean in general vector spaces. Ann. Prob. 7, 587–621.Google Scholar
[5] Donsker, M. D. and Varadhan, S. R. S. (1976) Asymptotic evaluation of certain Markov process expectations for large time III. Commun. Pure Appl. Math. 29, 389–461.Google Scholar
[6] Groeneboom, P., Oosterhoff, J. and Ruymgaart, F. H. (1979) Large deviations for empirical probability measures. Ann. Prob. 7, 553–586.Google Scholar
[7] Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, MA.Google Scholar
[8] Sanov, I. N. (1957) On the probability of large deviations of random variables (in Russian). Mat. Sb. 42, 11–44. (English translation in Selected Transl. Math. Statist. Prob. (1961) 1, 213-244.)Google Scholar
[9] Varadhan, S. R. S. (1984) Large Deviations and Applications. SIAM, Philadelphia.Google Scholar