Noncommutative Stationary Processes

Quantum probability and the theory of operator algebras are bothconcerned 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, ontopicsincluding 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 isnew, but many interestingquestions are accessible even to the reader equipped only with basic knowledge of quantum probability and operator algebras.