Spherical harmonic analysis for multivariate stable distributions

Zhiyi Chi

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arXiv · 2010.04793

Spherical harmonic analysis for multivariate stable distributions

Zhiyi Chi

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Abstract

Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a practical setting is that for any distribution with stability index not equal to 1 and with a polynomial spectral spherical density, the series representation converges absolutely with all terms being calculable in closed form. Asymptotic expansions consisting of spherical harmonics are also considered for probability density functions.

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Zhiyi Chi. 2020-10-09. Spherical harmonic analysis for multivariate stable distributions. https://arxiv.org/abs/2010.04793

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