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White Noise on Bialgebras by Michael Schurmann (Paperback, 1993)

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White Noise on Bialgebras. Short Title WHITE NOISE ON BIALGEBRAS 1993. 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. Hudson and K.R. Parthasarathy.

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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. Hudson and 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 should 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 have some knowledge of functional analysis, operator algebras, and probability theory.