Determinisms of Stable Processes and their Applications

稳定分布有重尾。也就是说，所有人都期望高斯分布没有方差，其中一些没有均值。它们作为非高斯（重尾）现象的模型很重要。有一些例子具有被称为“决定论”的性质。如果存在一个自然数n，并且对于任何大于n的维分布，如果由它的n维边际分布所决定，我们称这个过程具有n维（弱）决定性，本文试图阐明决定性与过程结构之间的关系。我们得到，1。对于一类称为集指标过程的过程，其决定性是由欧氏几何中的除数定理导出的。并对一些具体的例子，证明了其整除数.存在两个不同的二维稳定分布的例子，其二维特征函数在扇形域内重合。

The stable distribution have heavy tails. That is, all of them expect the Gaussian distributions have no variance and some of them have no mean. They are important as models for non-Gaussian (heavy tailed) Phenomena. There exist some examples which have properties called "determinisms". If there exists a natural number n and if for any dimensional distribution higher than n is determined by it n-dimensional marginal distributions, we call that the process has "n-dimensional (weak) determinism".In this investigation, we have tried to clarify the relation between determinisms and the structure of the process. We get,1. For a class of processes called set-indexed process, the determinisms are derived from theorems of division numbers in Euclidean Geometry. And for some concrete examples, we obtain the division numbers with proofs.2. There exist examples of 2 different 2-dimensional stable distributions of which 2-dimensional characteristic functions are coincide inside a sectoral domain.