Stochastic integral representation theorem for quantum semimartingales.

DOI10.1016/S0022-1236(02)00027-7zbMath1036.60060MaRDI QIDQ1405086

Un Cig Ji

Publication date: 25 August 2003

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

zbMATH Keywords

Boson Fock spacequantum stochastic processquantum Itô formulaquantum stochastic integralquantum semimartingale

Mathematics Subject Classification ID

Generalizations of martingales (60G48) White noise theory (60H40) Quantum stochastic calculus (81S25)

Related Items (12)

Analytic characterizations of infinite dimensional distributions ⋮ Annihilation-derivative, creation-derivative and representation of quantum martingales ⋮ Stochastic integral representations of quantum martingales on multiple Fock space ⋮ White noise differential equations for vector-valued white noise functionals ⋮ INTEGRAL REPRESENTATION OF QUANTUM MARTINGALES ⋮ Quantum white noise stochastic analysis based on nuclear algebras of entire functions ⋮ Quantum stochastic calculus associated with quadratic quantum noises ⋮ An implementation problem for boson fields and quantum Girsanov transform ⋮ Quantum stochastic integral representations of Fock space operators ⋮ Characterization of S-transform for general construction of infinite-dimensional distributions ⋮ UNIQUENESS OF INTEGRANDS IN QUANTUM STOCHASTIC INTEGRAL ⋮ Wick calculus for vector-valued Gaussian white noise unctionals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum Ito's formula and stochastic evolutions
• A non-commutative martingale representation theorem for non-Fock quantum Brownian motion
• Fermion martingales
• Stochastic integral representation of bounded quantum martingales in Fock space
• Cohomology of power sets with applications in quantum probability
• The Ito-Clifford integral
• Quantum probability for probabilists
• Wick product of white noise operators and quantum stochastic differential equations.
• Quantum and non-causal stochastic calculus
• White noise calculus and Fock space
• An algebra of non-commutative bounded semimartingales: Square and angle quantum brackets
• On a dual pair of spaces of smooth and generalized random variables
• Generalized quantum stochastic processes on Fock space
• On the martingale property for generalized stochastic processes
• On characterizing quantum stochastic evolutions
• Quantum white noises—White noise approach to quantum stochastic calculus
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators
• REGULAR GENERALIZED FUNCTIONS IN GAUSSIAN ANALYSIS
• On Square Integrable Martingales
• A quantum nonadapted Ito formula and stochastic analysis in Fock scale

This page was built for publication: Stochastic integral representation theorem for quantum semimartingales.