White Noise Analysis and its Applications

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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.