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Asymptotic Expansion of Gaussian Chaos via Probabilistic Approach. 17 February, 2015;статья
- Авторы: Enkelejd Hashorva, Dmitry Korshunov, Piterbarg Vladimir I.
- Сборник: ArXiv.org.e-Print
- Серия: [math.PR]
- Том: 1708
- Год издания: 2017
- Издательство: Cornell University Press
- Местоположение издательства: United States
- Первая страница: 1
- Последняя страница: 31
- Аннотация: For a centered d-dimensional Gaussian random vector ξ=(ξ1,…,ξd) and a homogeneous function h:Rd→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