Invariant Markov Processes Under Lie Group Actions

Authors: Liao, Ming

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  • Author is an internationally recognized leader in the study of jump processes in stochastic differential geometry
  • Presents new research involving the interaction of several mathematical areas, such as stochastic analysis, differential geometry, Lie groups, measure theory, and harmonic analysis
  • Explores an intersection of probability theory and Lie group theory with potential for many future applications
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About this book

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 GA 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.

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Invariant Markov Processes Under Actions of Topological Groups

    Pages 1-34

    Liao, Ming

  • Lévy Processes in Lie Groups

    Pages 35-71

    Liao, Ming

  • Lévy Processes in Homogeneous Spaces

    Pages 73-101

    Liao, Ming

  • Lévy Processes in Compact Lie Groups

    Pages 103-133

    Liao, Ming

  • Spherical Transform and Lévy-Khinchin Formula

    Pages 135-167

    Liao, Ming

Buy this book

eBook n/a
  • ISBN 978-3-319-92324-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-319-92323-9
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-3-030-06406-8
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Invariant Markov Processes Under Lie Group Actions
Authors
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-92324-6
DOI
10.1007/978-3-319-92324-6
Hardcover ISBN
978-3-319-92323-9
Softcover ISBN
978-3-030-06406-8
Edition Number
1
Number of Pages
XIII, 363
Topics