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On a joint strong approximation theorem for record and inter-record times
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  • Published: 01 June 1987

On a joint strong approximation theorem for record and inter-record times

  • D. Pfeifer1,2 

Probability Theory and Related Fields volume 75, pages 213–221 (1987)Cite this article

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  • 15 Citations

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Summary

We present a simple joint strong approximation for the logarithms of record and inter-record times from an exchangeable sequence, including an exact estimation for the rate of convergence in terms of upper and lower class functions of a Wiener process. The approach chosen here allows for simple proofs of exact and asymptotic (joint) results for record and inter-record times, such as the Law of Large Numbers (LLN), Central Limit Theorem (CLT) and Law of the Iterated Logarithm (LIL), and others.

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References

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Author information

Authors and Affiliations

  1. Institut für Statistik und Wirtschaftsmathematik, Technische Universität Aachen, Wüllnerstrasse 3, D-5100, Aachen, Germany

    D. Pfeifer

  2. University of North Carolina at Chapel Hill, Chapel Hill, USA

    D. Pfeifer

Authors
  1. D. Pfeifer
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Additional information

Research supported by the Air Force Office of Scientific Research Contract No. F49620 85 C0144

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Cite this article

Pfeifer, D. On a joint strong approximation theorem for record and inter-record times. Probab. Th. Rel. Fields 75, 213–221 (1987). https://doi.org/10.1007/BF00354034

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  • Received: 17 October 1984

  • Revised: 05 November 1985

  • Published: 01 June 1987

  • Issue Date: June 1987

  • DOI: https://doi.org/10.1007/BF00354034

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Keywords

  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
  • Central Limit
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