Analytic and Asymptotic Properties of Multivariate Generalized Linnik's Probability Densities

作者：Lim S C; Teo L P^*

来源：Journal of Fourier Analysis and Applications, 2010, 16(5): 715-747.

DOI：10.1007/s00041-009-9097-6

• Multivariate generalized Linnik distribution
• Characteristic function
• Liouville numbers
• Entire functions
• Asymptotic behavior

This paper studies the properties of the probability density function p(alpha,nu,n) (x) of the n-variate generalized Linnik distribution whose characteristic function phi(alpha,nu,n)(t) is given by
phi(alpha,nu,n)(t) = 1/ (1+parallel to t parallel to(alpha))(nu)' alpha epsilon (0,2), nu > 0, t epsilon R(n).
where parallel to t parallel to is the Euclidean norm of t is an element of R(n). Integral representations of p(alpha,nu,n) (x) are obtained and used to derive the asymptotic expansions of p(alpha,nu,n) (x) -> 0 and parallel to x parallel to -> infinity respectively. It is shown that under certain conditions which are arithmetic in nature, p(alpha,nu,n) (x) can be represented in terms of entire functions.

• 出版日期2010-10