Expansions for the Density of the Absolute Value of a Strictly Stable Vector.

摘要

Let q be the density function of the absolute value of a strictly stable random vector in R sup N, N-dimensional Euclidean space. Asymptotic expressions for q(r) for large r and for small r are found. The proofs use the Fourier inversion formula and contour integration. Bessel functions play a role occupied by the exponential and trigonometric functions when N = 1. (Author)