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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
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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

Information

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

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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