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Asymptotics and Bounds for Multivariate Gaussian Tails

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  • Enkelejd Hashorva

    (University of Bern)

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.

Suggested Citation

  • Enkelejd Hashorva, 2005. "Asymptotics and Bounds for Multivariate Gaussian Tails," Journal of Theoretical Probability, Springer, vol. 18(1), pages 79-97, January.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:1:d:10.1007_s10959-004-2577-3
    DOI: 10.1007/s10959-004-2577-3
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    References listed on IDEAS

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    1. Bischoff, Wolfgang & Hashorva, Enkelejd & Hüsler, Jürg & Miller, Frank, 2004. "On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 105-115, January.
    2. Mukherjea, Arunava & Stephens, Richard, 1990. "The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 95-115, July.
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    Cited by:

    1. Enkelejd Hashorva, 2010. "Boundary Non-crossings of Brownian Pillow," Journal of Theoretical Probability, Springer, vol. 23(1), pages 193-208, March.
    2. Das, Bikramjit & Fasen-Hartmann, Vicky, 2024. "On heavy-tailed risks under Gaussian copula: The effects of marginal transformation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    3. Bisewski, Krzysztof & Dȩbicki, Krzysztof & Kriukov, Nikolai, 2023. "Simultaneous ruin probability for multivariate Gaussian risk model," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 386-408.
    4. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "On heavy-tailed risks under Gaussian copula: the effects of marginal transformation," Papers 2304.05004, arXiv.org.

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