Asymptotics and Bounds for Multivariate Gaussian Tails

Enkelejd Hashorva
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Enkelejd Hashorva: University of Bern

Journal of Theoretical Probability, 2005, vol. 18, issue 1, 79-97

Abstract: 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.

Keywords: Tail asymptotics; Gaussian random sequences; Discrete boundary crossing; Brownian bridge; Quadratic programming (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-004-2577-3

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