Lévy Processes in Lie Groups

ISBN-13: 9780521836531 / Angielski / Twarda / 2004 / 276 str.

Ming Liao; Bela Bollobas; W. Fulton

Opis

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. This work provides 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.

Recenzje

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

Spis treści

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.