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White Noise Analysis and its Applications

白噪声分析及其应用

基本信息

批准号：
10045031
负责人：
HIDA Takeyuki
金额：
$ 1.86万
依托单位：
Meijo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
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

项目摘要

By the Research Project"White Noise Analysis and its Applications", the period : April 1998 March 2000, we obtained many results on White Noise Analysis and Quantum Probability Theory. We organized four international conferences on the infinite dimensional analysis. In December 1998, the Volterra Center organized the International Conference on Infinite Dimensional Analysis and Quantum Probability at University of Bari in Italy and all of members of this research project in Japan were attended and gave lectures. In March 1999, Meijo University organized the Second International Conference on Quantum Information and all menbers of this research project in Italy were invited. In July 1999, the Volterra Center organized an International Summer School "White Noise Approach to Classical and Quantum Stochastic Calculi and Quantum Probability" and all of members gave lectures. In March 2000, Meijo University organized the Third International Conference on Quantum Information and all of members gave lectures. Trough the conferences, we obtained developments, in particular, in the following subjects : 1) Stochastic Variational Equations, 2) White Noise Approaches to the Complexity, 3) Irreversibility on the Stochastic Process, 4) Stochastic Processes generated by functions of the Levy Laplacian, 5) Quantum Stochastic Analysis by the Stochastic Limit, 6) Mathematical model of the Quantum Computer, etc. White Noise Analysis give a basic idea to study Quantum Stochastic Analysis and also can give many applications to other fields. By a lot of achievements on White Noise Analysis until now, American Mathematical Society added one subject "60H40 : White Noise Theory" in the AMS Mathematics Subject Classifications 2000.

在1998年4月至2000年3月的课题“白噪声分析及其应用”中，我们在白噪声分析和量子概率论方面取得了许多成果。我们组织了四次关于无限维分析的国际会议。1998年12月，Volterra中心在意大利巴里大学组织了无限维分析和量子概率国际会议，该研究项目在日本的所有成员都参加了会议并发表了演讲。1999年3月，Meijo大学组织了第二届国际量子信息会议，邀请了在意大利参加这一研究项目的所有成员。1999年7月，Volterra中心组织了一次国际暑期学校，题为“经典和量子随机微积分的白噪声方法和量子概率”，所有成员都作了演讲。2000年3月，美穗大学组织召开了第三届国际量子信息会议，全体成员作了报告。通过这些会议，我们特别在以下方面取得了进展：1)随机变分方程，2)白噪声方法的复杂性，3)随机过程的不可逆性，4)由Levy Laplace函数产生的随机过程，5)随机极限下的量子随机分析，6)量子计算机的数学模型等。白噪声分析为研究量子随机分析提供了一个基本思想，也可以在其他领域有很多应用。到目前为止，美国数学学会在白噪声分析方面取得了许多成果，在2000年的AMS数学学科分类中增加了一门学科“60H40：白噪声理论”。