Sanov meets Cramér again |
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| Authors: | B. Gerritse |
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| Affiliation: | Dept. of Mathematics. University of Nijmegen. Toernooiveld 1, 6525 ED Nijmegen, The Netherlands |
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| Abstract: | We introduce a new method for proving large-deviation principles (LDPs). This method amounts to "mixing" a collection of LDPs with a sequence of probability measures that obeys itself an LDP. As an illustration, we construct from empirical measures a sequence of capacity-valued maps that can be considered as an indexed collection of LDPs. The index 1 coincides with Sanov's theorem. By taking a Poisson mixture we establish a new connection with Cramér's theorem. |
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| Keywords: | empirical measures capacities large deviations Sanov's theorem Cramér's theorem |
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