Research Catalog

Title

Lévy processes in Lie groups / Ming Liao.

Author

Liao, Ming.

Publication

Cambridge, UK ; New York : Cambridge University Press, c2004.

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Holdings

Details

Description

x, 266 p. : ill.; 24 cm.

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.

Series Statement

Cambridge tracts in mathematics ; 162

Uniform Title

Cambridge tracts in mathematics 162.

Subject

• Lie groups
• Lâevy processes
• Lévy processes

Bibliography (note)

• Includes bibliographical references (p. 261-263) and index.

Processing Action (note)

• committed to retain

Contents

1. Levy processes in Lie groups -- 2. Induced processes -- 3. Generator and stochastic integral equation of a Levy process -- 4. Levy processes in compact Lie groups and Fourier analysis -- 5. Semi-simple Lie groups of noncompact type -- 6. Limiting properties of Levy processes -- 7. Rate of convergence -- 8. Levy processes as stochastic flows -- A. Lie groups -- B. Stochastic analysis.

ISBN

0521836530

LCCN

^^2003066662

Owning Institutions

Harvard Library