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On the smallest maximal increment of partial sums of i.i.d. random variables
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  • Published: 01 May 1997

On the smallest maximal increment of partial sums of i.i.d. random variables

  • Uwe Einmahl1 &
  • David M. Mason2 

Probability Theory and Related Fields volume 108, pages 67–86 (1997)Cite this article

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Summary.

We study the almost sure limiting behavior of the smallest maximal increment of partial sums of \(n\) independent identically distributed random variables for a variety of increment sizes \(k_n\), where \(k_n\) is a sequence of integers satisfying \(1 \le \ k_n \le n\), and going to infinity at various rates. Our aim is to obtain universal results on such behavior under little or no assumptions on the underlying distribution function.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Uwe Einmahl

  2. Department of Mathematical Sciences, University of Delaware, 501 Ewing Hall, 19716, Newark, DE, USA

    David M. Mason

Authors
  1. Uwe Einmahl
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  2. David M. Mason
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Additional information

Received: 30 August 1995 / In revised form: 27 September 1996

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Cite this article

Einmahl, U., Mason, D. On the smallest maximal increment of partial sums of i.i.d. random variables. Probab Theory Relat Fields 108, 67–86 (1997). https://doi.org/10.1007/s004400050101

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  • Published: 01 May 1997

  • Issue Date: May 1997

  • DOI: https://doi.org/10.1007/s004400050101

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  • Mathematics Subject Classification (1991):60F15, 60E07
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