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Probability on Real Lie Algebras: Cambridge Tracts in Mathematics, cartea 206

Autor Uwe Franz, Nicolas Privault
en Limba Engleză Hardback – 25 ian 2016
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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Specificații

ISBN-13: 9781107128651
ISBN-10: 110712865X
Pagini: 302
Ilustrații: 2 b/w illus. 27 exercises
Dimensiuni: 152 x 229 x 21 mm
Greutate: 0.61 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:New York, United States

Cuprins

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.

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Descriere

This monograph is a progressive introduction to non-commutativity in probability theory.