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The uniform central limit theorem for the tent map

Author

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  • Bae, Jongsig
  • Hwang, Changha
  • Jun, Doobae

Abstract

This paper considers the asymptotic behaviors of the processes generated by the classical ergodic tent map that is defined on the unit interval. We get the uniform version of central limit theorem for the tent map by using the method of uniformly integrable entropy. An application to Kolmogorov–Smirnov type result is provided.

Suggested Citation

  • Bae, Jongsig & Hwang, Changha & Jun, Doobae, 2012. "The uniform central limit theorem for the tent map," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1021-1027.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:1021-1027
    DOI: 10.1016/j.spl.2012.02.003
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    References listed on IDEAS

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    1. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.
    2. Bae, Jongsig & Hwang, Changha & Jun, Doobae, 2010. "The uniform laws of large numbers for the tent map," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1437-1441, September.
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