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Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables

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  • Dianliang Deng

Abstract

Let be a sequence of i.i.d. real-valued random variables, and , . 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).

Suggested Citation

  • Dianliang Deng, 2009. "Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-15, November.
    • Handle: RePEc:hin:jijmms:253750
    DOI: 10.1155/2009/253750
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