Noncommutative stationary processes

Description:

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.

subjects: Noncommutative algebras,  Stationary processes,  Operator algebras,  Processus stationnaires,  Algèbres non commutatives,  Nichtkommutative Wahrscheinlichkeit,  Stationärer Prozess,  Functionaalanalyse,  Stationaire processen,  Stochastische processen,  Markov-processen,  Processus stationnaire,  Algèbre non commutative,  Mathematics,  Functional analysis,  Operator theory,  Distribution (Probability theory)