A nonadapted stochastic calculus and non stationary evolution in Fock scale

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dc.creatorBelavkin, V. P.
dc.date2005-12-21
dc.date.accessioned2026-07-07T06:55:39Z
dc.date.available2026-07-07T06:55:39Z
dc.descriptionA 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. 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 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.
dc.description27 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html http://www.maths.nott.ac.uk/personal/vpb/research/cha_noi.html
dc.identifierhttps://arxiv.org/abs/math/0512509
dc.identifierhttp://arxiv.org/abs/math/0512509
dc.identifierQuantum Probability and Related Topics 6 137--179 World Scientific, Singapore 1991
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106348
dc.subjectProbability
dc.subjectFunctional Analysis
dc.titleA nonadapted stochastic calculus and non stationary evolution in Fock scale
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