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- Title
Asymptotic expansion of Gaussian chaos via probabilistic approach.
- Authors
Hashorva, Enkelejd; Korshunov, Dmitry; Piterbarg, Vladimir
- Abstract
For a centered d-dimensional Gaussian random vector ξ = ( ξ, ... , ξ) and a homogeneous function h : ℝ → 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.
- Subjects
GAUSSIAN distribution; PROBABILITY theory; MATRICES (Mathematics); MATHEMATICS; POLYNOMIALS
- Publication
Extremes, 2015, Vol 18, Issue 3, p315
- ISSN
1386-1999
- Publication type
Article
- DOI
10.1007/s10687-015-0215-3