Noncommutative Stationary Processes

2004
ISBN: 978-3-540-20926-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1839, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Gohm, Rolf

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik

Inhaltsverzeichnis

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.