Noncommutative Stationary Processes
Gohm, Rolf.
Noncommutative Stationary Processes [electronic resource] / by Rolf Gohm. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1839 0075-8434 ; . - Lecture Notes in Mathematics, 1839 .
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.
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.
9783540399025
10.1007/b95349 doi
Distribution (Probability theory.
Functional analysis.
Operator theory.
Probability Theory and Stochastic Processes.
Functional Analysis.
Operator Theory.
QA273.A1-274.9 QA274-274.9
519.2
Noncommutative Stationary Processes [electronic resource] / by Rolf Gohm. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1839 0075-8434 ; . - Lecture Notes in Mathematics, 1839 .
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.
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.
9783540399025
10.1007/b95349 doi
Distribution (Probability theory.
Functional analysis.
Operator theory.
Probability Theory and Stochastic Processes.
Functional Analysis.
Operator Theory.
QA273.A1-274.9 QA274-274.9
519.2