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Hitsuda-Skorohod Quantum Stochastic Integrals in Terms of Quantum Stochastic Gradients(Micro-Macro Duality in Quantum Analysis)

Hitsuda-Skorohod Quantum Stochastic Integrals in Terms of Quantum Stochastic Gradients(Micro-Macro Duality in Quantum Analysis)
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UNIQUENESS OF INTEGRANDS IN QUANTUM STOCHASTIC INTEGRAL

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006
As a general study for uniqueness of integrands in quantum martingale representation, we present a necessary and sufficient condition for uniqueness of integrands in a quantum stochastic integral. Also, several equivalent conditions to the necessary and sufficient condition are studied.
Ji, Un Cig, Sinha, Kalyan B.
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Quantum Stochastic Integral Representations on Interacting Fock Space

Journal of Theoretical Probability, 2014
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Yuanbao Kang, Caishi Wang
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Stochastic path-integral simulation of quantum scattering

Physical Review A, 1993
We present a path-integral solution for the exact propagation of the Wigner distribution in phase space, which is an improved version of results obtained [Maslov, Bertrand, Combe, and co-workers, J. Sov. Math. 13, 315 (1980); 19, 55 (1982); Lett. Math. Phys. 7, 327 (1983); Physica 124A, 561 (1984)] and is suitable for Monte Carlo simulations.
, Schmidt, , Möhring
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Quantum stochastic integral representations of Fock space operators

Stochastics, 2009
An (unbounded) operator Ξ on Boson Fock space over L 2(R +) is called regular if it is an admissible white noise operator such that the conditional expectations give rise to a regular quantum martingale. We prove that an admissible white noise operator is regular if and only if it admits a quantum stochastic integral representation.
Un Çig Ji, Nobuaki Obata
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Quantum martingales and stochastic integrals

Lecture Notes in Mathematics, 1988
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Quantum stochastic integration and quantum stochastic differential equations

Mathematical Proceedings of the Cambridge Philosophical Society, 1994
AbstractQuantum stochastic integrals are constructed using the non-commutativeLp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution.
Barnett, Chris, Goldstein, Stanisław, Wilde, Ivan   +2 more
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Multidimensional Quantum Stochastic Integrals

AIP Conference Proceedings, 2011
Quantum stochastic analogues (H,A{Az}z∈R+,m,R+), of a classical stochastic base may be formed whereby a classical sample space Ω is replaced by a Hilbert Space H, σ‐field F is replaced by a von Neumann algebra b, the filtration {FI}i∈I by a filtration {Bz}z of von Neumann subalgebras of the von Neumann algebra B and the probability measure P with gage ...
William Joseph Spring, Timothy Ralph, Ping Koy Lam   +2 more
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A spectral approach to quantum stochastic integrals

Reports on Mathematical Physics, 1989
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Berezanskij, Yu. M., Zhernakov, N. V., Us, G. F.   +2 more
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The Wong-Zakai-Clifford quantum stochastic integral

Reports on Mathematical Physics, 1998
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Spring, William J., Wilde, Ivan F.
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