Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis : Burg (Spreewald), Germany, 15-20 March, 2001 / edited by W. Freudenberg.

Includes bibliographical references.

Preface; Contents; Markov Property -- Recent Developments on the Quantum Markov Property L. Accardi and F. Fidaleo; 1. Introduction; 2. The quantum Markov property on the spin algebra; 3. The relation with statistical mechanics; 4. Markov states on non homogeneous chains: general properties; 5. The structure of Markov states on chains: a reconstuction theorem; 6. Quantum Markov states on general quasi-local algebras; Acknowledgements; References; Quantum Boltzmann Statistics in Interacting Systems L. Accardi and S. Kozyrev; 1. Introduction

2. Quantum Boltzmann statistics for entangled operatorsAcknowledgements; References; Stationary Quantum Stochastic Processes from the Cohomological Point of View G. G. Amosov; 1. Introduction.; 2. Markovian perturbations of the group of shifts in L2(R).; 3. Stationary quantum stochastic process as *-homomorphism into a ring of cohomologies.; 4. Stationary quantum stochastic processes on the algebras of canonical commutation relations, the square of white noise relations and canonical anticommutation relations.; 5. Cocycle perturbations of K-flows and the Wold decomposition.; Acknowledgements

Asymptotic Behaviour of Markov Semigroups on Noncommutative L1- Spaces E. Yu. Emel'yanov and M. P. H. Wolff1. Introduction; 2. Main results; ACKNOWLEDGEMENT; References; Recognition and Teleportation K.-H. Fichtner, W. Freudenberg and M. Ohya; 1. Introduction; 2. Basic Notions; 3. Entangled States; 4. Channels; 5. The State of the Memory after Recognition; References; Prediction Errors and Completely Positive Maps R. Gohm; 1. Introduction; 2. Adapted isometrics; 3. Main results; 4. Finite-valued commutative processes; References; The Q-Product of Generalised Brownian Motions M. Guta

1. Introduction2. Generalised Brownian motions indexed by I and the -semigroup BP2I ( ); 3. The q-product of generalised Brownian motions; References; Multiplicative Properties of Double Stochastic Product Integrals R. L. Hudson; 1. Introduction.; 2. Preliminaries.; 3. Simple product integrals.; 4. Double product integrals.; References.; Markovianity of Quantum Random Fields in the B(H) Case V. Liebscher; 1. Conditional Independence; 2. Notations; 3. Quantum Conditional Independence; 4. Markov Properties on Undirected Graphs; Acknowledgements; References

This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, quantum Markov processes, the stochastic limit, quantum teleportation and other areas.

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