Lévy Processes in Lie Groups (Cambridge Tracts in Mathematics)
Publisher: Cambridge University Press
Published: May 10, 2004
Language: eng
Format: Hardcover
Number of pages: 276
ISBN-13: 9780521836531
Subjects: Linear algebra; Science/Mathematics; Lie groups; Mathematics; General; Mathematics / Differential Equations; Levy processes; Differential Equations; Lâevy processes
First sentence: This chapter contains an introduction to Levy processes in a general Lie group.
Description: 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.