Noncommutative Stationary Processes

Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, this book presents (without many prerequisites) some basic problems of interest to both fields, on topics including extensions and dilations of completely positive maps, Markov property and adaptedness, endomorphisms of operator algebras and the applications arising from the interplay of these themes. Much of the material is new, but many interesting questions are accessible even to the reader equipped only with basic knowledge of quantum probability and operator algebras.

List of contents

Preface.- Introduction.- 1. Extensions and dilations.- 2. Markov processes.- 3. Adaptedness.- 4. Examples and applications.- A. Some facts about unital completely positive maps.- References.- Index.

Summary

Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, this book presents (without many prerequisites) some basic problems of interest to both fields, on topics including extensions and dilations of completely positive maps, Markov property and adaptedness, endomorphisms of operator algebras and the applications arising from the interplay of these themes. Much of the material is new, but many interesting questions are accessible even to the reader equipped only with basic knowledge of quantum probability and operator algebras.

Product details

• Authors: R. Gohm, Rolf Gohm
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 18.03.2004
• EAN: 9783540209263
• ISBN: 978-3-540-20926-3
• No. of pages: 172
• Dimensions: 156 mm x 229 mm x 12 mm
• Weight: 284 g
• Illustrations: VIII, 172 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Stochastik, B, Funktionalanalysis und Abwandlungen, Mathematics and Statistics, Functional Analysis, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory, Functional analysis & transforms, Operator Theory