Generalizations of infinite dimensional Laplacians, construction methods of stochastic processes and developments in quantum information analysis

无限维拉普拉斯算子的推广、随机过程的构造方法以及量子信息分析的发展

• 批准号: 21540151
• 负责人: SAITO Kimiaki
• 金额: $ 2.16万
• 依托单位: Meijo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540151/
• 关键词: 無限次元ラプラス作用素; 無限次元確率過程; 確率過程構成法; 量子情報解析; Exotic Laplacian; レヴィ・ラプラシアンの一般化; ホワイトノイズの高階微分; チェサロヒルベルト空間

In this research, we considered a quantization and a new approach to a quantum information analysis by researching the infinite dimensional stochastic analysis jointly from major fields : probability theory, analysis, graph theory, number theory and computer science. Especially we succeeded in constructing the theory of higher order derivatives of white noise based on the stochastic analysis associated with exotic Laplacians defined by higher order Cesaro means of the second differentiation. It is a quite important progress and a creative point that a quantum information analysis in this direction can be constructed.

在这项研究中，我们通过研究主要领域的无限维度随机分析来考虑一种量化信息分析的量化和新方法：概率理论，分析，图理论，数字理论和计算机科学。尤其是我们成功地基于与由高级塞萨罗（Cesaro）第二分化平均值所定义的异国情调的拉普拉斯人相关的随机分析构建了白噪声的高阶理论。可以构建量子信息分析是一个非常重要的进步和创造力。

项目成果

Exotic laplacians and associated stochastic processes

• DOI: 10.1142/s0219025709003513
• 发表时间: 2009-03
• 期刊: Infinite Dimensional Analysis, Quantum Probability and Related Topics
• 作者: L. Accardi;U. Ji;Kimiaki Saitô

IMPROVEMENT OF HOWARD'S POLICY ITERATION METHOD FOR APPLICATION TO POLICIES MODELED BY PERIODIC, MARKOV CHAINS

霍华德策略迭代方法的改进，适用于周期性马尔可夫链建模的策略

• 发表时间: 2011
• 期刊: Far East Journal of Mathematical Sciences
• 作者: Negri;I. and Nishiyama;Y.;K.Saito (with Y.Uchimura)
• 通讯作者: K.Saito (with Y.Uchimura)

Stationary Distributions of the Bernoulli Type Galton-Watson Branching Process with Immigration

伯努利型高尔顿-沃森分支过程的平稳分布与移民

• 发表时间: 2011
• 期刊: Communications on Stochastic Analysis
• 作者: Y. Uchimura;K. Saito
• 通讯作者: K. Saito

A stationary distribution of the Bernoulli type Galton-Watson branching process with immigration

具有迁移的伯努利型高尔顿-沃森分支过程的平稳分布

• 发表时间: 2011
• 期刊: Communications on Stochastic Analysis
• 作者: 河上肇;土谷正明;K.Saito (with Y.Uchimura)
• 通讯作者: K.Saito (with Y.Uchimura)

Exotic Laplacians in White Noise Theory

白噪声理论中的奇异拉普拉斯算子

• 发表时间: 2009
• 作者: 入山聖史;大矢雅則;K. Saito
• 通讯作者: K. Saito