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Invariant Markov Processes Under Lie Group Actions

  • Ming Liao

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ming Liao
    Pages 35-71
  3. Ming Liao
    Pages 73-101
  4. Ming Liao
    Pages 103-133
  5. Ming Liao
    Pages 239-278
  6. Ming Liao
    Pages 305-329
  7. Back Matter
    Pages 331-363

About this book

Introduction

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.

Keywords

Lévy processes Lie groups homogeneous spaces Lévy-Khinchin formula martingale representation stochastic differential geometry

Authors and affiliations

  • Ming Liao
    • 1
  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-92324-6
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-92323-9
  • Online ISBN 978-3-319-92324-6
  • Buy this book on publisher's site
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