Coverart for item
The Resource White noise on bialgebras, Michael Schürmann

White noise on bialgebras, Michael Schürmann

Label
White noise on bialgebras
Title
White noise on bialgebras
Statement of responsibility
Michael Schürmann
Creator
Subject
Language
eng
Summary
Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudsonand K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book will be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should havesome knowledge of functional analysis, operator algebras, and probability theory
Member of
Action
digitized
Cataloging source
SPLNM
http://library.link/vocab/creatorDate
1955-
http://library.link/vocab/creatorName
Schürmann, Michael
Dewey number
530.1/2/015192
Index
index present
LC call number
  • QC174.17.M35
  • QA3
LC item number
  • S3 1993
  • .L28 no. 1544
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Lecture notes in mathematics,
Series volume
1544
http://library.link/vocab/subjectName
  • Quantum theory
  • Stochastic analysis
  • Théorie quantique
  • Analyse stochastique
  • Quantum theory
  • Stochastic analysis
  • Weißes Rauschen
  • Hopf-Algebra
  • Kwantummechanica
  • Bialgebra
  • Stochastische analyse
Label
White noise on bialgebras, Michael Schürmann
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 138-142) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Basic concepts and first results. 1.2. Quantum probabilistic notions. 1.3. Independence. 1.4. Commutation factors. 1.5. Invariance of states. 1.6. Additive and multiplicative white noise. 1.7. Involutive bialgebras. 1.9. White noise on involutive bialgebras -- 2. Symmetric white noise on Bose Fock space. 2.1. Bose Fock space over L[superscript 2](R[subscript+], H). 2.2. Kernels and operators. 2.3. The basic formula. 2.4. Quantum stochastic integrals and quantum Ito's formula. 2.5. Coalgebra stochastic integral equations -- 3. Symmetrization. 3.1. Symmetrization of bialgebras. 3.2. Schoenberg correspondence. 3.3. Symmetrization of white noise -- 4. White noise on Bose Fock space. 4.1. Group-like elements and realization of white noise. 4.2. Primitive elements and additive white noise. 4.3. Azema noise and quantum Wiener and Poisson processes. 4.4. Multiplicative and unitary white noise
  • 4.5. Cocommutative white noise and infinitely divisible representations of groups and Lie algebras -- 5. Quadratic components of conditionally positive linear functionals. 5.1. Maximal quadratic components. 5.2. Infinitely divisible states on the Weyl algebra -- 6. Limit theorems. 6.1. A coalgebra limit theorem. 6.2. The underlying additive noise as a limit. 6.3. Invariance principles
Control code
298690882
Dimensions
unknown
Extent
1 online resource (146 pages).
Form of item
online
Isbn
9783540476146
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)298690882
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Label
White noise on bialgebras, Michael Schürmann
Publication
Bibliography note
Includes bibliographical references (pages 138-142) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1. Basic concepts and first results. 1.2. Quantum probabilistic notions. 1.3. Independence. 1.4. Commutation factors. 1.5. Invariance of states. 1.6. Additive and multiplicative white noise. 1.7. Involutive bialgebras. 1.9. White noise on involutive bialgebras -- 2. Symmetric white noise on Bose Fock space. 2.1. Bose Fock space over L[superscript 2](R[subscript+], H). 2.2. Kernels and operators. 2.3. The basic formula. 2.4. Quantum stochastic integrals and quantum Ito's formula. 2.5. Coalgebra stochastic integral equations -- 3. Symmetrization. 3.1. Symmetrization of bialgebras. 3.2. Schoenberg correspondence. 3.3. Symmetrization of white noise -- 4. White noise on Bose Fock space. 4.1. Group-like elements and realization of white noise. 4.2. Primitive elements and additive white noise. 4.3. Azema noise and quantum Wiener and Poisson processes. 4.4. Multiplicative and unitary white noise
  • 4.5. Cocommutative white noise and infinitely divisible representations of groups and Lie algebras -- 5. Quadratic components of conditionally positive linear functionals. 5.1. Maximal quadratic components. 5.2. Infinitely divisible states on the Weyl algebra -- 6. Limit theorems. 6.1. A coalgebra limit theorem. 6.2. The underlying additive noise as a limit. 6.3. Invariance principles
Control code
298690882
Dimensions
unknown
Extent
1 online resource (146 pages).
Form of item
online
Isbn
9783540476146
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)298690882
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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