Quantum Probability Communications : Qp-Pq (Volumes 11).

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Attal, S.
Otros Autores: Lindsay, J. M.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific Publishing Company, 2003.
Colección:Qp-Pq: Quantum Probability & White Noise Analysis S.
Temas:
Probabilities.
Quantum theory.
Probabilités.
Théorie quantique.
probability.
Probabilities
Quantum theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • CONTENTS
  • CONTENTS of QPC XII
  • PREFACE for QPC Volumes XI & XII
  • EXTENSIONS OF QUANTUM STOCHASTIC CALCULUS
  • 1. ABSTRACT ITÃ? CALCULUS ON FOCK SPACE
  • 1.1. Short notations.
  • 1.2. ItÃ? calculus on Fock space.
  • 1.3. The ItÃ? integral is really an integral.
  • 1.4. Probabilistic interpretations of Fock space.
  • 2. EXTENSION OF QUANTUM STOCHASTIC CALCULUS
  • 2.1. A heuristic approach to noise.
  • 2.2. Extension of quantum stochastic integrals.
  • 2.3. Back to probabilistic interpretations.
  • 3. THE ALGEBRA OF REGULAR QUANTUM SEMIMARTINGALES
  • 3.1. Everywhere defined quantum stochastic integrals.3.2. The algebra of regular quantum semimartingales.
  • 3.3. Quantum brackets.
  • 4. SOME RECENT DEVELOPMENTS
  • 4.1. Functional quantum ItÃ? formulae.
  • 4.2. A remarkable transform of quantum processes.
  • BIBLIOGRAPHICAL NOTES
  • REFERENCES
  • QUANTUM ITÃ? ALGEBRAS: AXIOMS, REPRESENTATIONS, DECOMPOSITIONS
  • 0. INTRODUCTION
  • 1. REPRESENTATIONS OF ITÃ? *-ALGEBRAS
  • 2. TWO BASIC ITÃ? B*-ALGEBRAS
  • 3. DECOMPOSITION OF ITÃ? B*-ALGEBRAS
  • REFERENCES
  • FREE PROBABILITY FOR PROBABILISTS
  • 0. INTRODUCTION1. 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 ALGEBRASREFERENCES
  • 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

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