We introduce rank-k-continuous axis-aligned p-generalized elliptically contoured distributions and study their properties such as stochastic representations, moments, and density-like representations. Applying the Kolmogorov existence theorem, we prove the existence of random processes having axis-aligned p-generalized elliptically contoured finite dimensional distributions with arbitrary location and scale functions and a consistent sequence of density generators of p-generalized spherical invariant distributions. Particularly, we consider scale mixtures of rank-k-continuous axis-aligned p-generalized elliptically contoured Gaussian distributions and answer the question when an n-dimensional rank-k-continuous axis-aligned p-generalized elliptically contoured distribution is representable as a scale mixture of n-dimensional rank-k-continuous p-generalized Gaussian distribution for a suitable mixture distribution of a positive random variable. Based on this class of multivariate probability distributions, we introduce scale mixed p-generalized Gaussian processes having axis-aligned finite dimensional distributions being p-generalizations of elliptical random processes. Additionally, some of their characteristic properties are discussed and approximates of trajectories of several examples such as p-generalized Student-t and p-generalized Slash processes having axis-aligned finite dimensional distributions are simulated with the help of algorithms to simulate rank-k-continuous axis-aligned p-generalized elliptically contoured distributions.

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关于p广义椭圆随机过程

我们介绍了k阶连续k轴对齐的p广义椭圆形轮廓分布，并研究了它们的属性，例如随机表示，矩和密度类似的表示。应用Kolmogorov存在定理，我们证明了随机过程的存在，该过程具有轴对齐的p广义椭圆形椭圆形有限尺寸分布，具有任意位置和尺度函数，以及p广义球形不变分布的密度生成器的一致序列。尤其，我们考虑秩为k的连续k轴对齐的p广义椭圆轮廓的高斯分布的比例混合，并回答了以下问题：当n维秩为k的连续轴对齐的p广义椭圆轮廓的分布可以表示为的比例混合n维k阶连续k广义高斯分布，用于正随机变量的适当混合分布。基于此类的多变量概率分布，我们引入了比例混合的p广义高斯过程，其中轴对齐的有限维分布是椭圆随机过程的p广义化。另外，