Lévy Processes in Lie Groups

Up-to-the minute research on important stochastic processes.

Ming Liao (Author)

9780521836531, Cambridge University Press

Hardback, published 10 May 2004

276 pages
23.6 x 16.1 x 2.3 cm, 0.53 kg

'… an outstanding addendum to the literature on modern probability theory.' Mathematical Reviews

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.

1. Lévy processes in Lie groups
2. Generator and stochastic integral equation of a Lévy process
3. Semi-simple Lie groups of non-compact type
4. Limiting properties of Lévy processes
5. Rate of convergence
6. Lévy processes as stochastic flows.

Subject Areas: Calculus & mathematical analysis [PBK]