White Noise on Bialgebras

Michael Schürmann (auth.)3540566279, 9783540566274, 0387566279

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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Table of contents :
Introduction….Pages 1-11
Basic concepts and first results….Pages 12-40
Symmetric white noise on Bose Fock space….Pages 41-68
Symmetrization….Pages 69-80
White noise on bose fock space….Pages 81-113
Quadratic components of conditionally positive linear functionals….Pages 114-127
Limit theorems….Pages 128-137