Invariant Markov Processes Under Lie Group Actions

• Main Author: Liao, Ming (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Probabilities.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Probability Theory and Stochastic Processes.; Topological Groups, Lie Groups.; Global Analysis and Analysis on Manifolds.

The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on...

Table of Contents:

• Invariant Markov processes under actions of topological groups
• Lévy processes in Lie groups
• Lévy processes in homogeneous spaces
• Lévy processes in compact Lie groups
• Spherical transform and Lévy-Khinchin formula
• Inhomogeneous Lévy processes in Lie groups
• Proofs of main results
• Inhomogenous Lévy processes in homogeneous spaces
• Decomposition of Markov processes
• Appendices
• Bibliography
• Index.