A Coupling, and the Darling-Erdos Conjectures

Details A Coupling, and the Darling-Erdos Conjectures A Coupling, and the Darling-Erdos Conjectures

2005-11-17

arxiv.org/abs/math/0511429v1

Mathematics

Probability

13 pages

Scientific paper

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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