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What is Invariant Markov Processes Under Lie Group Actions about?

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 o

Who reads Invariant Markov Processes Under Lie Group Actions?

Author

Ming Liao

Publisher

Springer International Publishing : Imprint : Springer

Published

2018

Language

EN

ISBN

9783319923239

Category

nonfiction

Subjects

Mathematics, Stem