White Noise on Bialgebras

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.