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Asymptotic expansion of Gaussian chaos via probabilistic approachстатья
- Авторы: Hashorva Enkelejd, Korshunov Dmitry, Piterbarg Vladimir I.
- Журнал: Extremes
- Том: 18
- Год издания: 2015
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- DOI: 10.1007/s10687-015-0215-3
- Аннотация: 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.
- Добавил в систему: Питербарг Владимир Ильич