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Large deviations for the empirical process of a symmetric measure: a lower bound

Daras Tryfonas

Πλήρης Εγγραφή

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Περίληψη

Let {Xj}j=1∞ be a sequence of r.v.'s defined on a probability space (Ω,F,μ) and taking values in a compact metric space S, let Full-size image (<1 K) with X(n,ω) the point in SZ obtained by repeating (X1(ω),…,Xn(ω)) periodically on both sides and T the shift on SZ, be the empirical process associated to {Xj}j=1∞. We prove here that a large deviations result in the distributions of the empirical process w.r.t. a certain measure μ. This gives large deviations for the distributions of the empirical process with respect to a symmetric measure and also those associated to an exchangeable sequence of r.v.'s.

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