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.

稳定分布有较重的尾部。也就是说，它们都期望高斯分布没有方差有些没有均值。它们是非高斯（重尾）现象的重要模型。存在一些具有“决定论”性质的例子。如果存在一个自然数n，并且对于任何大于n的维分布都由它的n维边际分布决定，我们称该过程具有“n维（弱）决定论”。在这次调查中，我们试图澄清决定论和过程结构之间的关系。我们得到1。对于一类被称为集索引过程的过程，从欧几里得几何中的除数定理导出了决定论。对于一些具体的例子，我们用证明得到了除法数。存在两个不同的二维稳定分布的例子，其中二维特征函数在一个扇形域中重合。

项目成果

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.

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.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)。