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Asymptotic expansion of Gaussian chaos via probabilistic approach

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>09/2015
Issue number3
Number of pages33
Pages (from-to)315-347
Publication StatusPublished
Early online date10/03/15
<mark>Original language</mark>English


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.