Determinisms of Stable Processes and their Applications

稳定过程的决定论及其应用

• 批准号: 10640142
• 负责人: TAKENAKA Shigeo
• 金额: $ 1.92万
• 依托单位: Okayama University Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640142/
• 关键词: Stable systems; Symmetric stable processes; Determinisms; Integral Geometry; Division number; 安定過程; 確率過程の決定性; SαS-Processes; Sat-indexed process

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.

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。

项目成果

T. Deck, J. Potthof, G. Vage & H. Watanabe: "Stability of Solutions of Parabolic PDEs with Random Drift and Viscosity Limit"Appl Math Optim. 40. 393-416 (1999)

T. 戴克、J. 波特霍夫、G. 瓦奇

S.Kamiya: "On discrete subgroups of PU(1,2 : C)with Heisenberg translation"J. London Math. Soc.(in printing).

S.Kamiya：“关于 PU(1,2 : C) 的离散子群与海森堡翻译”J.

S.Takenaka: "On determinism of set-indexed S α S-processes"in"Trends in probability and related analysis 1999". 285-290 (1999)

S.Takenaka：“论集合索引 S α S 过程的决定论”，《概率和相关分析趋势 1999》285-290 (1999)。

K.Hasegawa, T.Ikeda & T.Kikuchi: "Commuting difference operators arising from the elliptic C^{(1)}_2-face model"J. Math Phys. 44. 4545-4568 (1999)

长谷川 K、池田 T

S.Takenaka: "On determinisms of set indexed SαS-processes" Trends in Probability and Related Analysis. To appear. (1999)

S.Takenaka：“关于集合索引 SαS 过程的决定论”概率和相关分析的趋势 (1999)。