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Asymptotic expansion of Gaussian chaos via probabilistic approach

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Asymptotic expansion of Gaussian chaos via probabilistic approach. / Hashorva, Enkelejd; Korshunov, Dmitry; Piterbarg, Vladimir I.
In: Extremes, Vol. 18, No. 3, 09.2015, p. 315-347.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Hashorva, E, Korshunov, D & Piterbarg, VI 2015, 'Asymptotic expansion of Gaussian chaos via probabilistic approach', Extremes, vol. 18, no. 3, pp. 315-347. https://doi.org/10.1007/s10687-015-0215-3

APA

Hashorva, E., Korshunov, D., & Piterbarg, V. I. (2015). Asymptotic expansion of Gaussian chaos via probabilistic approach. Extremes, 18(3), 315-347. https://doi.org/10.1007/s10687-015-0215-3

Vancouver

Hashorva E, Korshunov D, Piterbarg VI. Asymptotic expansion of Gaussian chaos via probabilistic approach. Extremes. 2015 Sept;18(3):315-347. Epub 2015 Mar 10. doi: 10.1007/s10687-015-0215-3

Author

Hashorva, Enkelejd ; Korshunov, Dmitry ; Piterbarg, Vladimir I. / Asymptotic expansion of Gaussian chaos via probabilistic approach. In: Extremes. 2015 ; Vol. 18, No. 3. pp. 315-347.

Bibtex

@article{054cad26894449c9bb068159b67a3116,
title = "Asymptotic expansion of Gaussian chaos via probabilistic approach",
abstract = "For a centered d-dimensional Gaussian random vector ξ = (ξ 1, … , ξ d ) and a homogeneous function h : ℝ d → ℝ we derive asymptotic expansions for the tail of the Gaussian chaos h(ξ) given the function h is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of h(ξ) and its density at infinity and then discuss possible extensions for some general ξ with polar representation.",
keywords = "Wiener chaos, Polynomial chaos, Gaussian chaos, Multidimensional normal distribution, Subexponential distribution, Determinant of a random matrix, Gaussian orthogonal ensemble, Diameter of random Gaussian clouds, Max-domain of attraction",
author = "Enkelejd Hashorva and Dmitry Korshunov and Piterbarg, {Vladimir I.}",
year = "2015",
month = sep,
doi = "10.1007/s10687-015-0215-3",
language = "English",
volume = "18",
pages = "315--347",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Asymptotic expansion of Gaussian chaos via probabilistic approach

AU - Hashorva, Enkelejd

AU - Korshunov, Dmitry

AU - Piterbarg, Vladimir I.

PY - 2015/9

Y1 - 2015/9

N2 - For a centered d-dimensional Gaussian random vector ξ = (ξ 1, … , ξ d ) and a homogeneous function h : ℝ d → ℝ we derive asymptotic expansions for the tail of the Gaussian chaos h(ξ) given the function h is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of h(ξ) and its density at infinity and then discuss possible extensions for some general ξ with polar representation.

AB - For a centered d-dimensional Gaussian random vector ξ = (ξ 1, … , ξ d ) and a homogeneous function h : ℝ d → ℝ we derive asymptotic expansions for the tail of the Gaussian chaos h(ξ) given the function h is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of h(ξ) and its density at infinity and then discuss possible extensions for some general ξ with polar representation.

KW - Wiener chaos

KW - Polynomial chaos

KW - Gaussian chaos

KW - Multidimensional normal distribution

KW - Subexponential distribution

KW - Determinant of a random matrix

KW - Gaussian orthogonal ensemble

KW - Diameter of random Gaussian clouds

KW - Max-domain of attraction

U2 - 10.1007/s10687-015-0215-3

DO - 10.1007/s10687-015-0215-3

M3 - Journal article

VL - 18

SP - 315

EP - 347

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 3

ER -