Asymptotic expansion of Gaussian chaos via probabilistic approach

作者：Hashorva Enkelejd; Korshunov Dmitry; Piterbarg Vladimir I

来源：Extremes, 2015, 18(3): 315-347.

DOI：10.1007/s10687-015-0215-3

• 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

For a centered d-dimensional Gaussian random vector xi = (xi(1),..., xi (d) ) and a homogeneous function h : R-d -> R we derive asymptotic expansions for the tail of the Gaussian chaos h(xi) 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(xi) and its density at infinity and then discuss possible extensions for some general xi with polar representation.

• 出版日期2015-9