Quantum probability communications [[electronic resource] ] : QP-PQ . Volume 11 / / managing editors, Stephane Attal, J. Martin Lindsay

• Record Nr.: UNINA9910824440203321
• Pubbl/distr/stampa: New Jersey, : World Scientific, c2003
• ISBN: 1-281-92813-5; 9786611928131; 981-277-541-2
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (314 p.)
• Collana: Quantum probability communications ; ; v. 11
• Altri autori (Persone): AttalS (Stephane); LindsayJ. Martin
• Disciplina: 530.12
• Soggetti: Probabilities; Quantum theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""0. INTRODUCTION""""1. LARGE MATRICES""; ""2. FREE RANDOM VARIABLES""; ""3. FREE CONVOLUTION""; ""4. THEORY OF ADDITION OF FREE RANDOM VARIABLES""; ""5. SPEICHER'S COMBINATORIAL APPROACH TO FREENESS""; ""6. SOME FURTHER TOPICS""; ""ACKNOWLEDGMENT""; ""REFERENCES""; ""CONDITIONAL EXPECTATIONS ON VON NEUMANN ALGEBRAS""; ""0. INTRODUCTION""; ""1. THE NONCOMMUTATIVE CONDITIONAL EXPECTATION""; ""2. GENERALISED CONDITIONAL EXPECTATIONS""; ""3. CANONICAL STATE EXTENSIONS""; ""4. STOCHASTIC TRANSITIONS FOR VON NEUMANN ALGEBRAS""; ""5. AN APPLICATION: MARKOVIANITY FOR STATES ON MUTUALLY COMMUTING VON NEUMANN ALGEBRAS""""REFERENCES""; ""CLASSICAL PROBABILITY THEORY AN OUTLINE OF STOCHASTIC INTEGRALS AND DIFFUSIONS""; ""First Lecture (One hour)""; ""BROWNIAN MOTIONS""; ""FURTHER READING""; ""Second Lecture (One hour)""; ""MARTINGALES""; ""FURTHER READING""; ""Third Lecture (One and a half hour)""; ""SEMIMARTINGALES AND STOCHASTIC INTEGRATION""; ""FURTHER READING""; ""Fourth Lecture (One and a half hour)""; ""THE CHANGE OF VARIABLE FORMULA; STOCHASTIC DIFFERENTIAL EQUATIONS""; ; ""FURTHER READING""; ""Fifth Lecture (One and a half hour)""""MARKOV PROCESSES, DIFFUSIONS AND FLOWS""; ""FURTHER READING""; ""Sixth Lecture (One and a half hour)""; ""ITERATED STOCHASTIC INTEGRALS, STRUCTURE EQUATIONS""; ""FURTHER READING""; ""ACKNOWLEDGEMENTS""; ""QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS""; ""0. INTRODUCTION""; ""1. QUANTUM STOCHASTIC CALCULUS""; ""2. TIME REVERSAL AND DUAL COCYCLES""; ""3. QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS""; ""4. MINIMAL QUANTUM DYNAMICAL SEMIGROUP""; ""5. THE RESOLVENT OF THE MINIMAL SEMIGROUP""; ""6. CONSERVATIVITY""; ""7. UNITARY SOLUTIONS""; ""8. INNER QUANTUM FLOWS""
• Sommario/riassunto: Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12. Contents:Extensions of Quantum Stochastic Calculus (S Attal)Quantum Itô; Algebras: Axioms, Representations, Decompositions (V B