A quantum nonadapted Ito formula and stochastic analysis in Fock scale
نویسندگان
چکیده
منابع مشابه
A Quantum Nonadapted Itô Formula and Stochastic Analysis in Fock Scale
A 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 spac...
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In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field FX, of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally...
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Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...
متن کاملA stochastic double product in non-Fock quantum stochastic calculus
Generalising the previous Fock case, we show that in an extremal universally invariant representation of the canonical commutation relations, a second quantised double product of infinitesimal rotations is a stochastic double product in the corresponding non-Fock quantum stochastic calculus. AMS Subject Classification 81S25.
متن کاملSome Properties of Quantum Lévy Area in Fock and Non-fock Quantum Stochastic Calculus.
We consider the analogue of Lévy area, de ned as an iterated stochastic integral, obtained by replacing the two independent component onedimensional Brownian motions by the mutually non-commuting momentum and position Brownian motions P and Q of either Fock or non-Fock quantum stochastic calculus, which are also stochastically independent in a certain sense. We show that the resulting quantum L...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1991
ISSN: 0022-1236
DOI: 10.1016/0022-1236(91)90129-s