Author	Schรผrmann, Michael. author
Title	White Noise on Bialgebras [electronic resource] / by Michael Schรผrmann
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect to	http://dx.doi.org/10.1007/BFb0089237
Descript	VI, 146 p. online resource

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

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

1. Mathematics
2. Algebra
3. Mathematical analysis
4. Analysis (Mathematics)
5. Probabilities
6. Physics
7. Mathematics
8. Probability Theory and Stochastic Processes
9. Analysis
10. Theoretical
11. Mathematical and Computational Physics
12. Algebra