Probability on Real Lie Algebras
Probability on Real Lie Algebras
Nicolas Privault, Nanyang Technological University, Singapore
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.
- Explains the connection between fundamental algebraic structures and probability distributions
- Covers specialized topics based on recent research
- Most chapters are accompanied with exercises and their solutions
Product details
No date availableHardback
9781107128651
302 pages
229 × 152 × 21 mm
0.6kg
2 b/w illus. 27 exercises
Table of Contents
- Introduction
- 1. Boson fock space
- 2. Real Lie algebras
- 3. Basic probability distributions on Lie algebras
- 4. Noncommutative random variables
- 5. Noncommutative stochastic integration
- 6. Random variables on real Lie algebras
- 7. Weyl calcuus on real Lie algebras
- 8. Lévy processes on real Lie algebras
- 9. A guide to the Malliavin calculus
- 10. Noncommutative Girsanov theorem
- 11. Noncommutative integration by parts
- 12. Smoothness of densities on real Lie algebras
- Appendix
- Exercise solutions.
