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On the maximum of a Wiener process and its location
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  • Published: December 1987

On the maximum of a Wiener process and its location

  • E. Csáki1,
  • A. Földes1 &
  • P. Révész2 

Probability Theory and Related Fields volume 76, pages 477–497 (1987)Cite this article

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  • 5 Citations

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Summary

Consider a Wiener process {W(t),t≧0}, letM(t)=max |W(s)| andv(t) be the location of the maximum of the absolute value of\(\mathop {W( \cdot )}\limits^{ 0\mathop< \limits_ = s\mathop< \limits_ = t} \) in [0,t] i.e.|W(v(t))|=M(t). We study the limit points of (α t M(t),β t v(t)) ast→∞ where α t and β t are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval ofM(t).

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, Reáltanoda u 13-15, H-1053, Budapest, Hungary

    E. Csáki & A. Földes

  2. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität, Wiedner Hauptstr. 8, A-1040, Wien, Austria

    P. Révész

Authors
  1. E. Csáki
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  2. A. Földes
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  3. P. Révész
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Additional information

Research supported by Hungarian National Foundation for Scientific Research Grant n. 1808

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Cite this article

Csáki, E., Földes, A. & Révész, P. On the maximum of a Wiener process and its location. Probab. Th. Rel. Fields 76, 477–497 (1987). https://doi.org/10.1007/BF00960069

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  • Received: 02 April 1985

  • Issue Date: December 1987

  • DOI: https://doi.org/10.1007/BF00960069

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Limit Point
  • Wiener Process
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