Noncommutative Stationary Processes

Rolf Gohm (auth.)3540209263, 9783540209263

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.

Table of contents :
Introduction….Pages 1-7
1 Extensions and Dilations….Pages 9-36
2 Markov Processes….Pages 37-71
3 Adaptedness….Pages 73-111
4 Examples and Applications….Pages 113-147
Appendix A: Some Facts about Unital Completely Positive Maps….Pages 149-163
References….Pages 165-168