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White noise on bialgebras /

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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: Schürmann, Michael, 1955-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [1993]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1544.
Subjects:
Quantum theory > Mathematics.
Stochastic analysis.
Théorie quantique > Mathématiques.
Analyse stochastique.
Kwantummechanica.
Stochastische analyse.
Wei€es Rauschen.
Hopf-Algebra.
Bialgebra.
Electronic books.
Online Access:Connect to the full text of this electronic book
Description
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.
Item Description:Electronic resource.
Physical Description:1 online resource (146 pages)
Format: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.
Bibliography:Includes bibliographical references (pages [138]-142) and index.
ISBN:9783540476146 (electronic bk.)
3540476148 (electronic bk.)
ISSN:0075-8434 ;