论文标题
用于多元稳定分布的球形谐波分析
Spherical harmonic analysis for multivariate stable distributions
论文作者
论文摘要
在各种条件下，获得了由球形谐波组成的串联表示，以及多元稳定分布的概率密度函数。可能适用于实际环境的ESULT是，对于任何稳定性指数不等于1并且具有多项式光谱球形密度的分布，该系列表示绝对收敛，所有术语均可以封闭形式计算。还考虑了由球形谐波组成的渐近扩展，以用于概率密度函数。
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.
