A Filtration of Wick Algebra and Its Application
to Quantum SDEs |
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| Authors: | Email author" target="_blank">Cai?Shi?WangEmail author Zhi?Yuan?Huang |
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| Institution: | (1) School of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China;(2) Department of Mathematics, Huazhong University of Science & Technology, Wuhan 430074, P. R.China |
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| Abstract: | A family of closed subalgebras, indexed by R (the set of real numbers), of the Wick algebra
is constructed. Fundamental properties of the family are shown including the increasing property and
the right–continuity. The notion of adaptedness to the family is defined for quantum stochastic processes
in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is
established for quantum stochastic differential equations in terms of generalized operators.
Supported by National Natural Science Foundation of China (10171035), Natural Science Foundation of Gansu
Province and NWNU-KJCXGC-212 |
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| Keywords: | White noise Wick algebra Filtration |
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