On probabilities of moderate deviations of sums of independent random variables

The asymptotics of probabilities of moderate deviations and their logarithm are investigated for an array of row-wise independent random variables with finite variations and finite one-sided moments of order $p>2$. The range of a zone of normal convergence is calculated in terms of Lyapunov ratios constructed from positive parts of the random variables. Bounds for probabilities of moderate deviations are also derived when the normal convergence fails.