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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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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 ...
Joseph Spring, Timothy C Ralph
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Quantum Stochastic Integrals

1984
There have been many attempts to set up quantum analogues of the theory of stochastic processes and stochastic differential equations. I should mention the many papers of M. Lax [1] on “quantum noise”, and those of Senitzky [2]; these were inspired by the problem of describing a laser, and by quantum electronics.
R F Streater, Streater R F
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Quasi-free quantum stochastic integrals in the plane

Reports on Mathematical Physics, 2002
In the classical theory of stochastic integration, Wong and Zakai followed by Cairoli and Walsh, developed a calculus for two-parameter martingales in the seventies. Here, the authors provide quantum analogues of that kind of integrals and calculus, involving two-parameter processes like quasi-free boson or fermion creation and annihilation.
Spring, W. J., Wilde, I. F.
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Algebraic theory of product integrals in quantum stochastic calculus

Journal of Mathematical Physics, 2000
Motivated by the search for solutions of the quantum Yang–Baxter equation, an algebraic theory of quantum stochastic product integrals is developed. The product integrators are formal power series in an indeterminate h whose coefficients are elements of the Lie algebra ℒ labelling the usual integrators of a many-dimensional quantum stochastic calculus.
R L Hudson
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Stochastic path integrals and open quantum systems

Physical Review A, 1996
Walter T Strunz
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Quantum martingales and stochastic integrals

Lecture Notes in Mathematics, 1988
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Euclidean quantum mechanics and stochastic integrals

Lecture Notes in Mathematics, 1981
R F Streater, Streater R F
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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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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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