Lévy processes in Lie groups
Author(s)
Bibliographic Information
Lévy processes in Lie groups
（Cambridge tracts in mathematics, 162）
Cambridge University Press, 2004
Available at / 39 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:512.482/L6132080004404
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Note
Includes bibliographical references (p. 261-263) and index
Description and Table of Contents
Description
The theory of Levy processes in Lie groups is not merely an extension of the theory of Levy 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 Levy processes in general Lie groups, the limiting properties of Levy 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.
Table of Contents
- 1. Levy processes in Lie groups
- 2. Generator and stochastic integral equation of a Levy process
- 3. Semi-simple Lie groups of non-compact type
- 4. Limiting properties of Levy processes
- 5. Rate of convergence
- 6. Levy processes as stochastic flows.
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