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In this paper we obtain a Bernstein type inequality for a class of weaklydependent and bounded random variables. The proofs lead to a moderatedeviations principle for sums of bounded random variables with exponentialdecay of the strong mixing coeficients that complements the large deviationresult obtained by Bryc and Dembo (1998) under superexponential mixing rates.

Bernstein inequality and moderate deviations under strong mixing conditions