An algebra of non-commutative bounded semimartingales: Square and angle quantum brackets

DOI10.1006/jfan.1994.1109zbMath0814.60059OpenAlexW2094588713MaRDI QIDQ1340814

Stéphane Attal

Publication date: 20 December 1994

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

Full work available at URL: https://doi.org/10.1006/jfan.1994.1109

zbMATH Keywords

Radon measuresnon-commutative stochastic calculusbounded operators on a Fock spacenon- commutative semimartingalesquantum martingal representation theorem

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Stochastic analysis (60H99) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items (10)

Quantum stochastic calculus with maximal operator domains. ⋮ Annihilation-derivative, creation-derivative and representation of quantum martingales ⋮ Non-commutative chaotic expansion of Hilbert-Schmidt operators on Fock space ⋮ Stochastic integral representation theorem for quantum semimartingales. ⋮ Stochastic integral representations of second quantization operators. ⋮ INTEGRAL REPRESENTATION OF QUANTUM MARTINGALES ⋮ Quantum \(\Omega\)-semimartingales and stochastic evolutions ⋮ Quantum stochastic integral representations of Fock space operators ⋮ UNIQUENESS OF INTEGRANDS IN QUANTUM STOCHASTIC INTEGRAL ⋮ From Pauli matrices to quantum Itô formula

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