Large deviations for empirical measures with degenerate limiting distribution |
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Authors: | Terence Chan |
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Institution: | (1) Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EH14 4AS Edinburgh, UK |
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Abstract: | Summary This paper studies the large deviations of the empirical measure associated withn independent random variables with a degenerate limiting distribution asn. A large deviations principle — quite unlike the classical Sanov type results — is established for such empirical measures in a general Polish space setting. This result is applied to the large deviations for the empirical process of a system of interacting particles, in which the diffusion coefficient vanishes as the number of particles tends to infinity. A second way in which the present example differs from previous work on similar weakly interacting systems is that there is a singularity in the mean-field type interaction. |
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Keywords: | 60F10 |
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