White Noise on Bialgebras

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....

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Bibliographic Details
Main Author Schurmann, Michael
Format eBook
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin / Heidelberg 2006
Springer Berlin Heidelberg
Springer
Edition1
SeriesLecture Notes in Mathematics
Subjects
Algebra
Analysis
Distribution (Probability theory
Global analysis (Mathematics)
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quantum theory-Mathematics
Theoretical, Mathematical and Computational Physics
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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.
ISBN:3540566279
9783540566274
9783662215142
3662215144
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0089237