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Probability on real Lie algebras

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations...

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Detalles Bibliográficos
Autores principales: Franz, Uwe, Privault, Nicolas
Lenguaje:eng
Publicado: Cambridge University Press 2016
Materias:
Acceso en línea:https://dx.doi.org/10.1017/CBO9781316415054
http://cds.cern.ch/record/2126972
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author Franz, Uwe
Privault, Nicolas
author_facet Franz, Uwe
Privault, Nicolas
author_sort Franz, Uwe
collection CERN
description This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
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institution Organización Europea para la Investigación Nuclear
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publisher Cambridge University Press
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spelling cern-21269722021-04-21T19:49:27Zdoi:10.1017/CBO9781316415054http://cds.cern.ch/record/2126972engFranz, UwePrivault, NicolasProbability on real Lie algebrasMathematical Physics and MathematicsThis monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.Cambridge University Pressoai:cds.cern.ch:21269722016
spellingShingle Mathematical Physics and Mathematics
Franz, Uwe
Privault, Nicolas
Probability on real Lie algebras
title Probability on real Lie algebras
title_full Probability on real Lie algebras
title_fullStr Probability on real Lie algebras
title_full_unstemmed Probability on real Lie algebras
title_short Probability on real Lie algebras
title_sort probability on real lie algebras
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1017/CBO9781316415054
http://cds.cern.ch/record/2126972
work_keys_str_mv AT franzuwe probabilityonrealliealgebras
AT privaultnicolas probabilityonrealliealgebras