We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaussian families. In addition to several special results we present a general approach to isotropic distribution families that is based on density expansions in terms of special surface harmonics. We discuss the connections to stochastic processes on spheres, in particular random walks, discrete mixture representations derived from spherical diffusions, and the use of Markov representations for the mixing base to obtain representations for families of spherical distributions.

翻译：我们为欧几里得球场概率分布的参数组别,如冯米塞-费舍、华生和角高西安等获得离散混合物表示,除了若干特别结果外,我们还根据地表特殊口音密度的扩大,对异向分布组别提出一般办法。我们讨论了与球体外切碎过程的联系,特别是随机散行、球体扩散产生的离散混合物表示,以及利用Markov代表作为混合基地的混合基地,为球体分布组别获得代表。