A QUANTUM NONADAPTED ITO FORMULA AND STOCHASTIC-ANALYSIS IN FOCK SCALE

被引:45
作者
BELAVKIN, VP
机构
[1] Dipartimento di Matematica, Centro Matematico V. Volterra, Università di Roma II, Roma
关键词
D O I
10.1016/0022-1236(91)90129-S
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 {black star}-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. 1 The 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 {black star}-homomorphism property of the QS integrable generators, is proved. © 1991.
引用
收藏
页码:414 / 447
页数:34
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