(1) Department of Statistics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Abstract:
Let {Xn, n 1} be a sequence of centered Gaussian random vectors in , d 2. In this paper we obtain asymptotic expansions (n ) of the tail probability P{Xn >tn} with tn a threshold with at least one component tending to infinity. Upper and lower bounds for this tail probability and asymptotics of discrete boundary crossings of Brownian Bridge are further discussed.
1} be a sequence of centered Gaussian random vectors in 
, d 
) of the tail probability P{Xn >tn} with tn 
a threshold with at least one component tending to infinity. Upper and lower bounds for this tail probability and asymptotics of discrete boundary crossings of Brownian Bridge are further discussed.