Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2, Canada
Copyright © 2009 Dianliang Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a sequence of i.i.d. real-valued random
, . Convergence rates of moderate deviations are derived; that is, the rates of
convergence to zero of certain tail probabilities of the partial
sums are determined. For example, we obtain equivalent
conditions for the convergence of the series
, where , , and are taken from a broad class of functions. These results
generalize and improve some results of Li et al. (1992)
and some previous work of Gut (1980).