White noise on bialgebras
type: Item
instance of: scholarly article
title: White noise on bialgebras
zbMATH Open document ID: 0773.60100
author: Michael Schürmann
published in: Lecture Notes in Mathematics
publication date: 1993-06-16T00:00:00Z
review text: This book presents some recent improvements in the theory of quantum (noncommutative) probability theory, enclosed in a self-contained course on this topic, including a presentation of the rich algebraic structure that is needed. It is based on several recent works, mainly by R. L. Hudson and K. R. Parthasarathy, L. Accardi, P. Glockner, H. Maassens, W. von Waldenfels, and the author himself. The classical theory of processes with independent and stationary increments on a group becomes here a very general noncommutative theory of what is called ``white noise'' on bialgebras of Hopf algebras. (Hopf algebras generalize the ``quantum groups'' of some authors.) The main aim attained in this book is the characterization of such a general white noise as the solution of a quantum stochastic differential equation of R. L. Hudson and K. R. Parthasarathy. Additive white noise, infinitely divisible representations on Lie algebras, and Azéma noise are also characterized.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 204187
zbMATH Keywords: quantum probability theory
zbMATH Keywords: white noise
zbMATH Keywords: quantum stochastic differential equation
zbMATH Keywords: Hopf algebras
zbMATH Keywords: processes with independent and stationary increments
zbMATH Keywords: infinitely divisible representations
MaRDI profile type: Publication
DOI: 10.1007/BFB0089237
description: scientific article; zbMATH DE number 204187