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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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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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On Solutions of Quantum Stochastic Integral Equations

, 1986
Throughout the discussion, we employ the notation and concepts already introduced in [1]. Thus, we also adopt here the partial *-algebraic setting of that paper.
G. O. S. Ekhaguere
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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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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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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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Kang, Yuanbao, Wang, Caishi
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Causal structure of quantum stochastic integrators

Theoretical and Mathematical Physics, 1997
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Anticipating quantum stochastic integrals

Infinite Dimensional Analysis, Quantum Probability and Related Topics
Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise ...
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