Conditional large deviations for a sequence of words |
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Authors: | Matthias Birkner |
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Institution: | Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany |
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Abstract: | Cut an i.i.d. sequence (Xi) of ‘letters’ into ‘words’ according to an independent renewal process. Then one obtains an i.i.d. sequence of words, and thus the level 3 large deviation behaviour of this sequence of words is governed by the specific relative entropy. We consider the corresponding problem for the conditional empirical process of words, where one conditions on a typical underlying (Xi). We find that if the tails of the word lengths decay exponentially, the large deviations under the conditional distribution are almost surely again governed by the specific relative entropy, but the set of attainable limits is restricted. |
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Keywords: | 60F10 60G10 82D60 |
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