Analysis of functionals of stable processes depending on new noise

根据新噪声分析稳定过程的泛函

• 批准号: 23540153
• 负责人: SI Si
• 金额: $ 2.66万
• 依托单位: Aichi Prefectural University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540153/
• 关键词: ホワイトノイズ; 新ノイズ; 安定仮定; 重複度; ポアソン型; 安定過程; イタリア、ローマ; White noise; New noise; Stable process; Multiple Markov property; 超汎関数; 双対生

Our idea of the research of random complex phenomena is the so-called reductionism. We first obtain a system of independent random variables that contain the same information as that of the given random system so that the given random phenomena can be expressed as functions of the independent random variables just formed. We are ready to carry on the analysis of those functions in question. We have confirmed that the probability distributions of the system of independent random variables are limited either Gaussian or Poisson type under reasonable assumptions. We have studied the latter case where not so well known, and obtained good applications to stable stochastic processes.

我们对随机复杂现象的研究的思想是所谓的还原主义。我们首先获得一个独立随机变量的系统，该变量包含与给定随机系统相同的信息，以便可以将给定的随机现象表示为刚刚形成的独立随机变量的函数。我们准备对有关功能进行分析。我们已经证实，在合理的假设下，独立随机变量系统的概率分布都受到高斯或泊松类型的限制。我们研究了后一种情况，在后一种情况下，并在稳定的随机过程中获得了良好的应用。

项目成果

New noise with space parameter and its application

具有空间参数的新噪声及其应用

• 发表时间: 2011
• 作者: T. Hida;Si Si and Win Win Htay,;Si Si;K-S. Lee and Si Si;Si Si;Si Si;Si Si;Si Si;Keisuke Shiromoto;Si Si;石川 喜啓;Si Si
• 通讯作者: Si Si

A New Noise with space parameter and its characteristic properties

一种新的空间参数噪声及其特征

• 期刊: Proceedings of 32nd International Conference on Quantum Probability and Related Topics
• 作者: T. Hida;Si Si and Win Win Htay,;Si Si;K-S. Lee and Si Si;Si Si;Si Si;Si Si
• 通讯作者: Si Si

A noise of new type and its applications

一种新型噪声及其应用

• 发表时间: 2012
• 期刊: Ricerche di Matematica, Springer
• 作者: T. Hida;Si Si and Win Win Htay,
• 通讯作者: Si Si and Win Win Htay,

Introduction to Hida Distributions

飞驒发行版简介

• 发表时间: 2011
• 作者: T. Hida;Si Si and Win Win Htay,;Si Si;K-S. Lee and Si Si;Si Si;Si Si;Si Si;Si Si;Keisuke Shiromoto;Si Si;石川 喜啓;Si Si;石川喜啓;T. Hida and Si Si;Si Si
• 通讯作者: Si Si

A noise with space parameter and invariance of the class of intensities

具有空间参数和强度类别不变性的噪声

• 发表时间: 2012
• 期刊: Infinite dimensional Analysis, Quantum Probability and Related Topics
• 作者: T. Hida;Si Si and Win Win Htay,;Si Si;K-S. Lee and Si Si
• 通讯作者: K-S. Lee and Si Si