rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Invariant Markov Processes Under Lie Group Actions
  name:
    name part: Liao, Ming.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 363 p. online resource.
  abstract: 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.
  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.
  note: by Ming Liao.
  subject:
    topic: Probabilities
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Global Analysis and Analysis on Manifolds
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319923246
  identifier: https://doi.org/10.1007/978-3-319-92324-6
  record info:
    record creation date: 180628
    record change date: 20191025151714.0
    record identifier: 978-3-319-92324-6