Lévy processes in Lie groups / Ming Liao.

Format:

Book

Author/Creator:

Liao, Ming (Mathematician), author.

Series:

Cambridge tracts in mathematics ; 162.

Cambridge tracts in mathematics ; 162

Language:

English

Subjects (All):

Lévy processes.

Lie groups.

Physical Description:

1 online resource (x, 266 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2004.

Language Note:

English

Summary:

The theory of Lévy processes in Lie groups is not merely an extension of the theory of Lévy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties reveal a deep connection between the behaviour of the stochastic processes and the underlying algebraic and geometric structures of the Lie groups themselves. The purpose of this work is to provide an introduction to Lévy processes in general Lie groups, the limiting properties of Lévy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces. The reader is assumed to be familiar with Lie groups and stochastic analysis, but no prior knowledge of semi-simple Lie groups is required.

Contents:

Cover; Half-title; Title; Copyright; Contents; Preface; List of Symbols; Introduction; 1 Lévy Processes in Lie Groups; 2 Induced Processes; 3 Generator and Stochastic Integral Equation of a Lévy Process; 4 Lévy Processes in Compact Lie Groups and Fourier Analysis; 5 Semi-simple Lie Groups of Noncompact Type; 6 Limiting Properties of Lévy Processes; 7 Rate of Convergence; 8 Lévy Processes as Stochastic Flows; Appendix A Lie Groups; Appendix B Stochastic Analysis; Bibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-15008-6

1-280-47800-4

9786610478002

0-511-19542-7

0-511-19608-3

0-511-19404-8

0-511-31440-X

0-511-54662-9

0-511-19478-1

OCLC:

171138818