White Noise on Bialgebras

1993
ISBN: 978-3-540-56627-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1544, 146 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 248 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Schürmann, Michael

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

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.