Brownian motion; Gaussian process; regular variation; he paper is concerned with the supremum of a centered Gaussian process with stationary increments over a random interval. The main result provides the exact asymptotics of the tail of the supremum distribution in the case that the length of the interval is regularly varying. In addition, we obtain explicit lower and upper bounds for the prefactor.

Gaussian processes (msc 60G15), Large deviations (msc 60F10), Extreme value theory; extremal processes (msc 60G70)
Logistics (theme 3), Energy (theme 4)
CWI. Probability, Networks and Algorithms [PNA]

Dȩbicki, K.G, Zwart, A.P, & Borst, S.C. (2002). The supremum of a Gaussian process over a random interval. CWI. Probability, Networks and Algorithms [PNA]. CWI.