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.
| ISBN: | 9781107128651 |
| Publication date: | 2nd April 2016 |
| Author: | Uwe Franz, Nicolas Privault |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 302 pages |
| Series: | Cambridge Tracts in Mathematics |
| Genres: |
Probability and statistics Algebra Calculus and mathematical analysis Stochastics Quantum physics (quantum mechanics and quantum field theory) |
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.
Probability on Real Lie Algebras features in the following genres: Probability and statistics, Algebra, Calculus and mathematical analysis, Stochastics, Quantum physics (quantum mechanics and quantum field theory)
Probability on Real Lie Algebras is available in Hardback, Ebook
Probability on Real Lie Algebras was written by Uwe Franz, Nicolas Privault and published by Cambridge University Press
Probability on Real Lie Algebras has 302 pages
Yes it is part of Cambridge Tracts in Mathematics series