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QUANTUM STOCHASTIC CALCULUS ON BOOLEAN FOCK SPACE
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2004In this paper we establish a theory of stochastic integration with respect to the basic field operator processes in the Boolean case. This leads to a Boolean version of quantum Itô's product formula and has applications to the theory of dilations of quantum dynamical semigroups.
Ben Ghorbal, Anis, Schürmann, Michael
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Journal of Soviet Mathematics, 1991
The main aim of this paper is to introduce the reader into the quantum stochastic calculus in the symmetric Fock space from the stochastic processes point of view. The author discusses the quantum Itô formula, applications to probabilistic representations of solutions of differential equations, and applications to extensions of dynamical semigroups ...
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The main aim of this paper is to introduce the reader into the quantum stochastic calculus in the symmetric Fock space from the stochastic processes point of view. The author discusses the quantum Itô formula, applications to probabilistic representations of solutions of differential equations, and applications to extensions of dynamical semigroups ...
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Quantum stochastic calculus associated with quadratic quantum noises
Journal of Mathematical Physics, 2016We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals ...
Un Cig Ji, Kalyan B. Sinha
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Journal of Mathematical Physics, 1985
The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how the formalism of quantum stochastic calculus of Hudson and Parthasarathy allows, in a simple way, for constructing a large class of OVSP’s that in ...
BARCHIELLI, ALBERTO, G. Lupieri
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The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how the formalism of quantum stochastic calculus of Hudson and Parthasarathy allows, in a simple way, for constructing a large class of OVSP’s that in ...
BARCHIELLI, ALBERTO, G. Lupieri
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Quantum and non-causal stochastic calculus
Probability Theory and Related Fields, 1993The quantum stochastic calculus initiated by \textit{R. L. Hudson} and \textit{K. R. Parthasarathy} [Commun. Math. Phys. 93, 301-323 (1984; Zbl 0546.60058)], and the noncausal stochastic calculus originating with the papers of \textit{M. Hitsuda} [Proc. 2nd Japan-USSR Symp. Probab. Theory 2, 111-114 (1972)] and \textit{A. V.
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Classical Stochastic Processes from Quantum Stochastic Calculus
Journal of Mathematical Sciences, 2001Using multidimensional quantum stochastic calculus, the author constructs a (weak) one-parameter representation \(\tilde{j}_t\), \(t\in {\mathbb R}_+\), of the Lie algebra \(gl(N)\) of \(N\times N\) matrices, which is then extended to a representation \(\tilde{J}_t\), \(t\in {\mathbb R}_+\), of the universal enveloping algebra \({\mathcal U}(gl(N ...
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Quantum and non-causal stochastic calculus
Acta Mathematica Sinica, 1998The authors introduce a quantum Fermion stochastic integral for non adapted integrands. Their method makes use of Guichardet's representation of Fock spaces in the form \(L^2 (\Gamma)\), where \(\Gamma\) is taken as the set of all finite subsets of a given non-atomic, separable, \(\sigma\)-finite, measurable space.
Liang, Zongxia, Zheng, Mingli
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Malliavin calculus for quantum stochastic processes
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999The purpose of this note is to show that the idea of the Malliavin calculus can be applied to quantum stochastic processes. The authors prove first a Girsanov formula and by a differentiation of this they obtain an integration by parts formula. Using these, the authors give sufficient conditions for the Wigner density to belong to a Sobolev space of ...
Franz, Uwe +2 more
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1986
The basic integrator processes of quantum stochastic calculus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Ito’s formula are described.
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The basic integrator processes of quantum stochastic calculus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Ito’s formula are described.
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Deformations of Algebras Constructed using Quantum Stochastic Calculus
Letters in Mathematical Physics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hudson, R. L., Parthasarathy, K. R.
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