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Strong approximations of k-th records and k-th record times by Wiener processes
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  • Published: February 1988

Strong approximations of k-th records and k-th record times by Wiener processes

  • Paul Deheuvels1 

Probability Theory and Related Fields volume 77, pages 195–209 (1988)Cite this article

Summary

We develop several strong approximations for k-th records and k-th record times by Wiener processes. Our main result is that it is possible to approximate by the same Wiener process up to the almost sure rate O(log j), where j stands for the index of the observations, the k-th records, the logarithms of the k-th record times, and the logarithms of the k-th interrecord times. We also provide some limiting weak laws and obtain Berry-Esséen-type theorems for k-th record times.

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Authors and Affiliations

  1. L.S.T.A., Université Paris VI, 4 place Jussieu, F-75230, Paris Cedex 05, France

    Paul Deheuvels

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  1. Paul Deheuvels
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Deheuvels, P. Strong approximations of k-th records and k-th record times by Wiener processes. Probab. Th. Rel. Fields 77, 195–209 (1988). https://doi.org/10.1007/BF00334037

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  • Received: 08 January 1986

  • Revised: 05 October 1987

  • Issue Date: February 1988

  • DOI: https://doi.org/10.1007/BF00334037

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Wiener Process
  • Record Time
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