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.

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Bibliographic Information

Book Title: White Noise on Bialgebras
Authors: Michael Schürmann
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0089237
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1993
Softcover ISBN: 978-3-540-56627-4Published: 12 May 1993
eBook ISBN: 978-3-540-47614-6Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VI, 146
Topics: Probability Theory and Stochastic Processes, Analysis, Theoretical, Mathematical and Computational Physics, Algebra

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Table of contents (7 chapters)

Front Matter

Introduction

Basic concepts and first results

Symmetric white noise on Bose Fock space

Symmetrization

White noise on bose fock space

Quadratic components of conditionally positive linear functionals

Limit theorems

Back Matter

About this book