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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Received: 30 August 1995 / In revised form: 27 September 1996
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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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DOI: https://doi.org/10.1007/s004400050101