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- W2051264340 abstract "We review the basic concepts of quantum probability and revise the classical and quantum stochastic (QS) calculus using the universal Ito B*-algebra approach. A non-commutative generalization of Levy process is defined in Fock–Guichardet space in terms of the underlying B*-Ito modular algebra. The main notions and results of classical and QS analysis are reformulated in terms of the non-commutative but associative stochastic covariation of quantum integrals defined as sesquilinear forms adapted to a quantum Levy process in Fock space. The general semi-Markov QS dynamics is defined in terms of a hemigroup of semi-morphic transformations as adjoints to a semiunitary hemigroup resolving a QS Schrodinger equation in Fock space. The corresponding semi-Markov hemigroup of completely positive contractions resolving a quantum master equation with generalized Lindblad generator as a non-commutative analogue of Feller–Kolmogorov equation is derived by taking vacuum conditional expectation in Fock space." @default.
- W2051264340 created "2016-06-24" @default.
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- W2051264340 date "2011-11-21" @default.
- W2051264340 modified "2023-09-26" @default.
- W2051264340 title "Quantum Lévy–Itô algebras and non-commutative stochastic analysis" @default.
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- W2051264340 doi "https://doi.org/10.1080/17442508.2011.615934" @default.
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