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

Abstract

Let $q$ be the density function of the absolute value of a strictly stable random vector in $R^N, N$-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 $N = 1$.