A quantum nonadapted Ito formula and stochastic analysis in Fock scale
A quantum nonadapted Ito formula and stochastic analysis in Fock scale
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DOI：
10.1016/0022-1236(91)90129-s
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发表时间：
1991-12
影响因子：
1.7
通讯作者：
V. Belavkin
中科院分区：
文献类型：
--
作者：
V. Belavkin
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and dimensionality form in terms of Malliavin derivative on a projective Fock space, and their uniform continuity with respect to the inductive limite convergence is proved. A new form of QS calculus based on an inductive ★-algebraic structure in an indefinite space is developed and a nonadaptive generalization of the QS Ito formula for its representation in Fock space is derived.1The problem of solution of general QS evolution equations in a Hilbert space is solved in terms of the constructed operator representation of chronological products, defined in the indefinite space, and the isometry and∗-homomorphism property respectively for operators and maps of these solutions, corresponding to the peseudounitary and ★-homomorphism property of the QS integrable generators, is proved.
