A quantum nonadapted Ito formula and stochastic analysis in Fock scale

DOI10.1016/0022-1236(91)90129-SzbMath0737.60042MaRDI QIDQ5905442

Vyacheslav P. Belavkin

Publication date: 27 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

evolution equations in a Hilbert spaceMalliavin derivative on a projective Fock spacenoncommutative generalization of Itô stochastic calculusquantum stochastic

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Stochastic integrals (60H05)

Related Items (5)

The central limit theorem for the Smoluchovski coagulation model ⋮ Quantum stochastic integral representations on interacting Fock space ⋮ Poisson stochastic integration in Hilbert spaces. ⋮ Characterization of S-transform for general construction of infinite-dimensional distributions ⋮ A canonical dilation of the Schrödinger equation

Cites Work

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• Quantum Ito's formula and stochastic evolutions
• Generalized Brownian functionals and stochastic integrals
• Generalized Brownian functionals and the Feynman integral
• Generalized stochastic integrals and the Malliavin calculus
• Stochastic calculus with anticipating integrands
• The Ito algebra of quantum Gaussian fields
• Cohomology of power sets with applications in quantum probability
• A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space
• Quantum stochastic processes

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