A General Darling–Erdős Theorem in Euclidean Space

Gauthier Dierickx () and Uwe Einmahl ()
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Gauthier Dierickx: Vrije Universiteit Brussel
Uwe Einmahl: Vrije Universiteit Brussel

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 1142-1165

Abstract: Abstract We provide an improved version of the Darling–Erdős theorem for sums of i.i.d. random variables with mean zero and finite variance. We extend this result to multidimensional random vectors. Our proof is based on a new strong invariance principle in this setting which has other applications as well such as an integral test refinement of the multidimensional Hartman–Wintner LIL. We also identify a borderline situation where one has weak convergence to a shifted version of the standard limiting distribution in the classical Darling–Erdős theorem.

Keywords: Darling–Erdős theorem; Extreme value distribution; Hartman–Wintner LIL; Integral test; Strong invariance principle; Multidimensional version; Double truncation; 60F15; 60F17 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-016-0728-y

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