A Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock scale

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dc.creatorBelavkin, V. P.
dc.date2005-12-22
dc.date.accessioned2026-07-07T06:54:41Z
dc.date.available2026-07-07T06:54:41Z
dc.descriptionA generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and basis form in terms of Malliavin derivative on a projective Fock scale, and their uniform continuity and QS differentiability with respect to the inductive limit 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. 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 unitary and *-homomorphism property respectively for operators and maps of these solutions, corresponding to the pseudounitary and *-homomorphism property of the QS integrable generators, is proved.
dc.description28 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html and http://www.maths.nott.ac.uk/personal/vpb/research/cha_noi.html
dc.identifierhttps://arxiv.org/abs/math-ph/0512076
dc.identifierhttp://arxiv.org/abs/math-ph/0512076
dc.identifierJournal of Functional Analysis 102 (1991) No 2, 414--447
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106026
dc.subjectMathematical Physics
dc.titleA Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock scale
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