Journal of Theoretical Probability

, Volume 18, Issue 1, pp 79–97 | Cite as

Asymptotics and Bounds for Multivariate Gaussian Tails

  • Enkelejd HashorvaEmail author

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.


Tail asymptotics Gaussian random sequences Discrete boundary crossing Brownian bridge Quadratic programming 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of BernBernSwitzerland

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