Probability on Real Lie Algebras
eBook - PDF

Probability on Real Lie Algebras

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Probability on Real Lie Algebras

About this book

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

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Yes, you can access Probability on Real Lie Algebras by Uwe Franz,Nicolas Privault in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Dedication
  7. Table of contents
  8. Notation
  9. Preface
  10. Introduction
  11. 1 Boson Fock space
  12. 2 Real Lie algebras
  13. 3 Basic probability distributions on Lie algebras
  14. 4 Noncommutative random variables
  15. 5 Noncommutative stochastic integration
  16. 6 Random variables on real Lie algebras
  17. 7 Weyl calculus on real Lie algebras
  18. 8 Lévy processes on real Lie algebras
  19. 9 A guide to the Malliavin calculus
  20. 10 Noncommutative Girsanov theorem
  21. 11 Noncommutative integration by parts
  22. 12 Smoothness of densities on real Lie algebras
  23. Appendix
  24. Exercise solutions
  25. References
  26. Index