The Resource White noise on bialgebras, Michael Schürmann
White noise on bialgebras, Michael Schürmann
Resource Information
The item White noise on bialgebras, Michael Schürmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item White noise on bialgebras, Michael Schürmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (146 pages).
- 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
- Isbn
- 9783540476146
- Label
- White noise on bialgebras
- Title
- White noise on bialgebras
- Statement of responsibility
- Michael Schürmann
- 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
- 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
- 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
- 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.
Subject
- Bialgebra
- Hopf-Algebra
- Kwantummechanica
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Stochastic analysis
- Stochastic analysis
- Stochastic analysis
- Stochastische analyse
- Théorie quantique -- Mathématiques
- Weißes Rauschen
- Analyse stochastique
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/White-noise-on-bialgebras-Michael/zZHsurenQCs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/White-noise-on-bialgebras-Michael/zZHsurenQCs/">White noise on bialgebras, Michael Schürmann</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
