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• catalog abstract "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.".
• catalog contributor b4657345.
• catalog created "c1993.".
• catalog date "1993".
• catalog date "c1993.".
• catalog dateCopyrighted "c1993.".
• catalog description "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.".
• catalog description "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.".
• catalog description "Includes bibliographical references (p. [138]-142) and index.".
• catalog description "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.".
• catalog extent "146 p. ;".
• catalog hasFormat "White noise on bialgebras.".
• catalog identifier "0387566279 (New York : acid-free)".
• catalog identifier "3540566279 (Berlin : acid-free) :".
• catalog isFormatOf "White noise on bialgebras.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1544.".
• catalog isPartOf "Lecture notes in mathematics ; 1544".
• catalog issued "1993".
• catalog issued "c1993.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer-Verlag,".
• catalog relation "White noise on bialgebras.".
• catalog subject "530.1/2/015192 20".
• catalog subject "Algebra.".
• catalog subject "Distribution (Probability theory).".
• catalog subject "Global analysis (Mathematics).".
• catalog subject "Mathematical physics.".
• catalog subject "Mathematics.".
• catalog subject "QC174.17.M35 S3 1993".
• catalog subject "Quantum theory Mathematics.".
• catalog subject "Stochastic analysis.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog title "White noise on bialgebras / Michael Schürmann.".
• catalog type "text".