Research on Fractional Brownian Motions by the Quantum Probabilistic Method.

量子概率方法研究分数布朗运动。

• 批准号: 20740053
• 负责人: ASAI Nobuhiro
• 金额: $ 1.83万
• 依托单位: Aichi University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740053/
• 关键词: 量子確率論; 直交多項式; シーガル・バーグマン変換; 変形フォック空間; 変形Fock空間; Wilson系列の直交多項式; 解析関数空間; メリン変換; 一般化Segal-Bargmann変換; 非ガウス型バーグマン測度; 非ガウス型確率測度; Fock空間; Meixner族の確率分布; Segal-Bargmann変換; 非ガウス測度

Motivated by the classical Segal-Bargmann transform in Gaussian analysis, which has been recognized as a useful way for the analysis on the Boson Fock space, we have tried to examine the classical-quantum correspondence of random variables (stochastic processes) by constructing one-mode Fock spaces and Hilbert spaces of square integrable analytic functions with respect to non-Gaussian Bargmann measures. It is essentially related to the complex moment problem for the construction of non-Gaussian Bargmann measures. Due to this reason, it would be quite difficult to develop the general way to solve our problem in a fully general form. Therefore, in this research program our consideration has been restricted to several special cases containing the Wilson's family of orthogonal polynomials under the special choice of parameters, which is in the higher hierarchy than the Meixner's family. As a result, we have succeeded to construct several non-Gaussian Bargmann measures, explicitly.

在高斯分析中经典的西格尔-巴格曼变换的启发下，我们试图通过构造关于非高斯巴格曼测度的平方可积解析函数的单模Fock空间和希尔伯特空间来检验随机变量(随机过程)的经典-量子对应。它本质上与构造非高斯Bargmann测度的复矩问题有关。由于这个原因，很难用普遍的方法来完全地普遍地解决我们的问题。因此，在这个研究方案中，我们的考虑被限制在几种特殊的情况下，其中包含威尔逊族的正交多项式在参数的特殊选择下，它比Meixner族处于更高的层次。作为结果，我们成功地构造了几个显式的非高斯巴格曼度量。

项目成果

Probability Measures on C arising from Continuous Dual Hahn Polynomials with Special Parameters

具有特殊参数的连续双哈恩多项式产生的 C 的概率测度

• 发表时间: 2010
• 作者: Nobuhiro Asai;Nobuhiro ASAI;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro Asai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro Asai
• 通讯作者: Nobuhiro Asai

The Meixner operators on one-mode Fock space and related topics

单模 Fock 空间上的 Meixner 算子及相关主题

• 发表时间: 2009
• 作者: 中路貴彦;山本隆範;N.Honda;Nobuhiro Asai;Naofumi Honda;中路貴彦;Nobuhiro Asai
• 通讯作者: Nobuhiro Asai

ベッセル関数で表現される確率測度とその応用例について

关于贝塞尔函数表示的概率测度及其应用实例

• 发表时间: 2009
• 作者: Nobuhiro Asai;Nobuhiro ASAI;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro Asai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro ASAI
• 通讯作者: Nobuhiro ASAI

The subordinated probability measure associated with the Jacobi parameters

与雅可比参数相关的从属概率测度

• 发表时间: 2010
• 作者: Nobuhiro Asai;Nobuhiro ASAI;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI;Hiroshi Hirai;Nobuhiro Asai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro Asai;Hiroshi Hirai;Nobuhiro ASAI
• 通讯作者: Nobuhiro ASAI

Bargmann-like measures related with the classical orthogonal polynomials

与经典正交多项式相关的类 Bargmann 测度

• 发表时间: 2009
• 作者: 中路貴彦;山本隆範;N.Honda;Nobuhiro Asai
• 通讯作者: Nobuhiro Asai