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White Noise on Bialgebras : Lecture Notes in Mathematics - Michael Schurmann

White Noise on Bialgebras

Lecture Notes in Mathematics

Paperback Published: 12th May 1993
ISBN: 9783540566274
Number Of Pages: 146

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Stochastic processes with independent increments on a groupare generalized to the concept of "white noise" on a Hopfalgebra or bialgebra. The main purpose of the book is thecharacterization of these processes as solutions of quantumstochastic differential equations in the sense of R.L.Hudsonand K.R. Parthasarathy. The notes are a contributionto quantum probability but they are also related toclassical probability, quantum groups, and operatoralgebras. The Az ma martingales appear as examples of whitenoise on a Hopf algebra which is a deformation of theHeisenberg group.The book will be of interest to probabilists and quantumprobabilists. Specialists in algebraic structures who arecurious about the role of their concepts in probablilitytheory as well as quantum theory may find the bookinteresting. The reader should havesome knowledge offunctional analysis, operator algebras, and probabilitytheory.

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.

ISBN: 9783540566274
ISBN-10: 3540566279
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 146
Published: 12th May 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.84
Weight (kg): 0.23