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Large deviations for the empirical mean of associated random variables. (English) Zbl 1151.60013
Let \((X_n)_{n\geq1}\) be a strictly stationary sequence of associated random variables which are uniformly bounded. Under the assumption of an hyper-geometric decay of \(\sum_{j=n}^\infty\text{Cov}(X_1,X_j)\) and a boundedness assumption on the densities of the sample means \(\overline{X}_n=n^{-1}\sum_{i=1}^nX_i\) it is shown that the sequence \((\overline{X}_n)_{n\geq1}\) satisfies the large deviation principle.

60F10 Large deviations
60G15 Gaussian processes
Full Text: DOI
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