Journal of Guangxi Normal University(Natural Science Edition) ›› 2010, Vol. 28 ›› Issue (3): 20-23.

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A Strictly Stationary Associated Random Sequence Which Unsatisfythe Central Limit Theorem

JIA Bao-hua   

  1. School of Mathematics and Computer Science,Ningxia University,Yinchuan Ningxia 750021,China
  • Received:2010-03-10 Online:2010-09-20 Published:2023-02-06

Abstract: An example of a strictly stationary associated randomsequence which does not satisfy the central limit theorem and whose partial sums' variance grows in a defined regular way is constructed.The well-known example of N.Herrndorf is generalized and the optimality of conditions in the classical Newman's theorem is shown.

Key words: associated random sequences, central limit theorem, stationarity, slowly varying functions

CLC Number: 

  • O211.4
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