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Precise Asymptotics in Strong Limit Theorems for Self-normalized Sums of Multidimensionally Indexed Random Variables

  • Dianliang DengEmail author
  • Zhitao Hu
Part of the Fields Institute Communications book series (FIC, volume 76)

Abstract

The present paper discusses the precise asymptotic behaviours for the deviation probabilities of self-normalized sums of multidimensionally indexed random variables. The precise asymptotics for the general deviation probabilities are derived. Many known theorems for self-normalized sums of random variables can follow from the given results, and thus the precise asymptotics in the complete moment convergence, law of iterated logarithm and large deviation for self-normalized sums are generalized from one-dimensionally indexed random variables to multidimensionally indexed random variables.

Notes

Acknowledgements

The first author’s research is partly supported by the Natural Sciences and Engineering Research Council of Canada.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada
  2. 2.Department of Mathematics and InformationChang’An UniversityShanxiChina

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