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A Coupling, and the Darling-Erdos Conjectures

Davar Khoshnevisan·David A. Levin
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Abstract

We derive a new coupling of the running maximum of an Ornstein-Uhlenbeck process and the running maximum of an explicit i.i.d. sequence. We use this coupling to verify a conjecture of Darling and Erdos (1956).

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Davar Khoshnevisan, David A. Levin. 2005-11-17. A Coupling, and the Darling-Erdos Conjectures. https://arxiv.org/abs/math/0511429

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