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: Semigroups, Boundary Value Problems and Markov Processes
  name:
    name part: Taira, Kazuaki.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    edition: 2nd ed. 2014.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIX, 716 p. 149 illus. online resource.
  abstract: A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.
  table of contents: 1.Introduction and Main Results -- Part I Elements of Analysis -- 2.Elements of Probability Theory -- 3.Elements of Functional Analysis -- 4.Theory of Semigroups -- Part II Elements of Partial Differential Equations -- 5.Theory of Distributions -- 6.Sobolev and Besov Spaces -- 7.Theory of Pseudo-Differential Operators -- 8.Waldenfels Operators and Maximum Principles -- Part III Markov Processes, Semigroups and Boundary Value problems -- 9.Markov Processes, Transition Functions and Feller Semigroups -- 10.Feller Semigroups and Elliptic Boundary Value Problems -- 11.Proof of Theorem 1.3 -- 12.Markov Processes Revisited -- 13.Concluding Remarks -- Appendix: Boundedness of Pseudo-Differential Operators -- References -- Index.
  note: by Kazuaki Taira.
  subject:
    topic: Mathematics
  subject:
    topic: Harmonic analysis
  subject:
    topic: Functional analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Abstract Harmonic Analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Probability Theory and Stochastic Processes
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783662436967
  identifier: http://dx.doi.org/10.1007/978-3-662-43696-7
  record info:
    record creation date: 140807
    record change date: 20151103131813.0
    record identifier: 978-3-662-43696-7