Let {X n , n ≥ 1} be a sequence of centered Gaussian random vectors in \({\mathbb R}^{d}\) , d ≥ 2. In this paper we obtain asymptotic expansions (n → ∞) of the tail probability P{X n >t n } with t n ɛ \({\mathbb R}^{d}\) 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.
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Hashorva, E. Asymptotics and Bounds for Multivariate Gaussian Tails. J Theor Probab 18, 79–97 (2005). https://doi.org/10.1007/s10959-004-2577-3
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DOI: https://doi.org/10.1007/s10959-004-2577-3