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Erdős-Révész type bounds for the length of the longest run from a stationary mixing sequence
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  • Published: May 1987

Erdős-Révész type bounds for the length of the longest run from a stationary mixing sequence

  • Karl Grill1 

Probability Theory and Related Fields volume 75, pages 77–85 (1987)Cite this article

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  • 6 Citations

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Summary

Let {X n} be a sequence of random variables assuming only values 0 and 1. A run of ones is a sequence of ones not interrupted by zeroes and preceded and followed by zeroes (except at the boundaries of the original sequence). The length of a run and the longest run within the first n observations are defined in the natural way.

Erdős and Révész (1975) (cf. also Samarova 1981; Guibas and Odlyzko 1980) gave a description of the almost sure asymptotic behaviour of the length of the longest run of ones from a coin-tossing sequence (i.e., the X nare i.i.d. r.v. with P(X n=0)=P(X n=1)=1/2). The present paper aims to extend their result to a certain class of stationary mixing sequences.

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References

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  8. Révész, P.: Three problems on the length of increasing runs. Stochastic Processes Appl. 15, 169–179 (1983)

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Authors and Affiliations

  1. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, Wiedner Hauptstrasse 8-20, A-1040, Wien, Austria

    Karl Grill

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  1. Karl Grill
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Cite this article

Grill, K. Erdős-Révész type bounds for the length of the longest run from a stationary mixing sequence. Probab. Th. Rel. Fields 75, 77–85 (1987). https://doi.org/10.1007/BF00320082

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  • Received: 19 December 1985

  • Revised: 28 November 1986

  • Issue Date: May 1987

  • DOI: https://doi.org/10.1007/BF00320082

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Keywords

  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • Statistical Theory
  • Original Sequence
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