Bernstein inequality and moderate deviations under strong mixing   conditions
  In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong mixing coeficients that complements the large deviation result obtained by Bryc and Dembo (1998) under superexponential mixing rates. 
Florence Merlev\`ede, Magda Peligrad, and Emmanuel Rio
math.PR