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Quantum Stochastic Calculus Associated With Quantum Lévy White Noise
Mathematical Methods in the Applied SciencesABSTRACTWe establish the commutation relations of the quantum Lévy operators, consisting of the generalized Lévy Gross Laplacian and its adjoint, annihilation operator, creation operator, and the Lévy number operator. In particular, such quantum Lévy operators span a nonsolvable ‐Lie algebra.
Omar Alzeley +2 more
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Exponential formulae in quantum stochastic calculus
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1996The rigorous definition of time-ordered exponentials, solving quantum linear stochastic differential equations, is extended to Boson and Fermion stochastic calculi with infinitely many degrees of freedom. The relation to the classicalmultiplicative stochastic integral, solving the Doleans exponential equation, is discussed.
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Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 1998A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated.
Huang, Zhiyuan, Luo, Shunlong
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1990
We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as Open image in new window where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only ...
R L Hudson, P Shepperson
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We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as Open image in new window where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only ...
R L Hudson, P Shepperson
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2012
Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers fortunes and survival analysis, Just as commutative integration theory may be realised as a special case of the more general non-commutative theory for ...
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Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers fortunes and survival analysis, Just as commutative integration theory may be realised as a special case of the more general non-commutative theory for ...
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Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus
20061 Introduction 31.1 Three approaches to continual measurements 31.2 Quantum stochastic calculus and quantum optics 31.3 Some notations: operator spaces 42 Unitary evolution and states 52.1 Quantum stochastic calculus 5The Fock space 5The Weyl operators and the Bose fields 6Quantum stochastic integrals 92.2 The unitary system–field ...
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Quantum Stochastic Calculus and Applications — A Review
1998It has been a little more than a decade since this subject, as it is understood today, came into being with the seminal paper of Hudson and Parthasarathy [1]. Since then the subject has seen rapid development and many of these can be found in the monographs of Parthasarathy [2] and Meyer [3]. Here I want to discuss some of the more recent developments.
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A Guide to the Stochastic Network Calculus
IEEE Communications Surveys and Tutorials, 2015Amr Rizk
exaly