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Convergence rates in the strong law for bounded mixing sequences
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  • Published: June 1987

Convergence rates in the strong law for bounded mixing sequences

  • Henry Berbee1 

Probability Theory and Related Fields volume 74, pages 255–270 (1987)Cite this article

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Summary

Speed of convergence is studied for a Marcinkiewicz-Zygmund strong law for partial sums of bounded dependent random variables under conditions on their mixing rate. Though α-mixing is also considered, the most interesting result concerns absolutely regular sequences. The results are applied to renewal theory to show that some of the estimates obtained by other authors on coupling are best possible. Another application sharpens a result for averaging a function along a random walk.

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Authors and Affiliations

  1. Stichting Mathematisch Centrum, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Henry Berbee

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  1. Henry Berbee
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Berbee, H. Convergence rates in the strong law for bounded mixing sequences. Probab. Th. Rel. Fields 74, 255–270 (1987). https://doi.org/10.1007/BF00569992

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  • Received: 03 December 1984

  • Revised: 08 November 1985

  • Issue Date: June 1987

  • DOI: https://doi.org/10.1007/BF00569992

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Keywords

  • Stochastic Process
  • Random Walk
  • Probability Theory
  • Convergence Rate
  • Mathematical Biology
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