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Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums

  • T. Cacoullos
  • N. Papadatos
  • V. Papathanasiou
Part of the Trends in Mathematics book series (TM)

Abstract

Three simple proofs of the classical CLT are presented. The proofs are based on some basic properties of covariance kernels or ω-functions in conjunction with bounds for the total variation distance. Applications to random sum CLT’s are also given.

Key words and phrases

covariance kernels CLT random sums 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • T. Cacoullos
    • 1
  • N. Papadatos
    • 2
  • V. Papathanasiou
    • 1
  1. 1.Department of MathematicsUniversity of AthensPanepistemiopolisAthensGreece
  2. 2.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

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