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Probability on real Lie algebras / Uwe Franz and Nicolas Privault.

By: Franz, Uwe [author].
Contributor(s): Privault, Nicolas [author].
Material type: TextTextSeries: Cambridge tracts in mathematics ; 206.Publisher: New York : Cambridge University Press, 2016Description: xix, 281 pages : illustrations ; 24 cm.ISBN: 9781107128651 .Subject(s): Lie algebras | ProbabilitiesDDC classification: 512.482
Contents:
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 calculus on real Lie algebras -- 8.Levy 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 -- A.1.Polynomials -- A.2.Moments and cumulants -- A.3.Fourier transform -- A.4.Cauchy -- Stieltjes transform -- A.5.Adjoint action -- A.6.Nets -- A.7.Closability of linear operators -- A.8.Tensor products -- Exercise solutions -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12.
Summary: 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 Levy 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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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.482 F837 (Browse shelf) Available 137494
Total holds: 0

Includes bibliographical references and index.

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 calculus on real Lie algebras --
8.Levy 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 --
A.1.Polynomials --
A.2.Moments and cumulants --
A.3.Fourier transform --
A.4.Cauchy --
Stieltjes transform --
A.5.Adjoint action --
A.6.Nets --
A.7.Closability of linear operators --
A.8.Tensor products --
Exercise solutions --
Chapter 1 --
Chapter 2 --
Chapter 3 --
Chapter 4 --
Chapter 5 --
Chapter 6 --
Chapter 7 --
Chapter 8 --
Chapter 9 --
Chapter 10 --
Chapter 11 --
Chapter 12.

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 Levy 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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