A Coupling, and the Darling-Erdos Conjectures
  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). 
Davar Khoshnevisan (University of Utah) and David A. Levin (University   of Oregon)