White Noise Analysis and its Applications

通过1998年4月至2000年3月的“白色噪声分析及其应用”研究项目，我们在白色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，沃尔泰拉中心在意大利的巴里大学组织了“无限维分析和量子概率国际会议”，日本的这一研究项目的所有成员都出席了会议并作了演讲。1999年3月，名城大学组织了第二届国际量子信息会议，邀请了意大利所有参与该研究项目的成员。1999年7月，沃尔泰拉中心组织了“经典和量子随机微积分与量子概率的白色噪声方法”国际暑期学校，全体成员进行了讲座。2000年3月，明城大学组织了第三届国际量子信息会议，全体成员都作了演讲。通过这些会议，我们取得了一些进展，特别是在下列主题方面：1）随机变分方程，2）复杂性的白色噪声方法，3）随机过程的不可逆性，4）由Levy Laplacian函数产生的随机过程，5）随机极限的量子随机分析，6）量子计算机的数学模型，白色噪声分析为量子随机分析的研究提供了一个基本的思路，也可以在其他领域得到广泛的应用。美国数学学会在白色噪声分析的基础上，在2000年AMS数学学科分类中增加了一个学科“60 H40：白色噪声理论”。

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.