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Invariant Markov Processes Under Lie Group Actions

Invariant Markov Processes Under Lie Group Actions

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Invariant Markov Processes Under Lie Group Actions Synopsis

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 manifolds to present the most recent results in a developing area of stochastic analysis.  The author's discussion is structured with three different levels of generality:
- A Markov process in a Lie group G that is invariant under the left (or right) translations
- A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X
- A Markov process xt invariant under the non-transitive action of a Lie group G
A large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property.  Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas.

Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.

About This Edition

ISBN: 9783030064068
Publication date:
Author: Ming Liao
Publisher: Springer an imprint of Springer International Publishing
Format: Paperback
Pagination: 363 pages
Genres: Probability and statistics
Stochastics
Groups and group theory
Calculus and mathematical analysis

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