发表机构
Zhejiang Sci-Tech University（浙江理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究无限可分随机向量，定义径向极点C_X(t)并推导其变分公式，证明相关规则，明确其几何性质，还给出加性伽马射线模型下的有限多面体公式。
AI 中文摘要
设X为具有有限二阶矩和协方差矩阵Σ的中心化无限可分随机向量。我们将径向极点C_X(t)定义为<t,X>的右侧次伽马界中的最小尺度，其中该界的二次代理固定为真实方差t^TΣt。典型方向测度与独立的Beta(1,2)乘子给出了C_X的精确变分公式。所得的扩域函数是正齐次的，且在所有与协方差二次型兼容的齐次分母中逐点最小。我们证明了线性映射、卷积和莱维时间规则，并表明方向余项的完整族决定了X的分布。几何上，C_X介于矩生成函数域的闵可夫斯基泛函与莱维测度正支撑函数的三分之一之间；上界常数是紧的，其零集为极锥。该极点不必是次可加的。在全局指数矩和正定协方差下，它在球面上连续；而仅有限方差时，它在邻近方向上允许从0跳变到无穷。对于加性伽马射线模型，C_X等于域规度，且具有有限多面体公式。
英文摘要
Let X be a centered infinitely divisible random vector with finite second moment and covariance matrix Sigma. We define the radial pole C_X(t) as the smallest scale in a right sub-gamma bound for <t,X> whose quadratic proxy is fixed at the true variance t^T Sigma t. A canonical directional measure and an independent Beta(1,2) multiplier give an exact variational formula for C_X. The resulting extended-valued function is positive homogeneous and is pointwise least among all homogeneous denominators compatible with the covariance quadratic form. We prove linear-map, convolution, and Levy-time rules, and show that the full family of directional remainders determines the law of X. Geometrically, C_X lies between the Minkowski functional of the moment-generating-function domain and one third of the positive support function of the Levy measure; the upper constant is sharp, and the zero set is a polar cone. The pole need not be subadditive. It is continuous on the sphere under global exponential moments and positive-definite covariance, whereas finite variance alone permits a jump from zero to infinity in nearby directions. For additive gamma-ray models, C_X equals the domain gauge and has a finite-polytope formula.
Comments15 pages
