Liao M. Levy Processes in Lie Groups

Cambridge University Press, 2004. - 276 p.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. 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.Levi processes in Lie groups.
Induced processes.
Generator and stochastic integral equation of a Levy process.
Levy processes in compact Lie Groups and Fourier
analysis.
Semi-simple Lie groups of noncompact type.
Limiting properties of Levy processes.
Rate of convergence
Lévy processes as stochastic flows.