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Semigroups, Boundary Value Problems and Markov Processes

  • KazuakiĀ Taira

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Kazuaki Taira
    Pages 1-31
  3. Elements of Analysis

    1. Front Matter
      Pages 33-33
    2. Kazuaki Taira
      Pages 35-98
    3. Kazuaki Taira
      Pages 99-142
    4. Kazuaki Taira
      Pages 143-198
  4. Elements of Partial Differential Equations

    1. Front Matter
      Pages 199-199
    2. Kazuaki Taira
      Pages 201-283
    3. Kazuaki Taira
      Pages 285-311
    4. Kazuaki Taira
      Pages 313-360
    5. Kazuaki Taira
      Pages 361-408
  5. Markov Processes, Semigroups and Boundary Value Problems

    1. Front Matter
      Pages 409-409
    2. Kazuaki Taira
      Pages 547-561
    3. Kazuaki Taira
      Pages 563-589
    4. Kazuaki Taira
      Pages 591-604
  6. Back Matter
    Pages 605-716

About this book

Introduction

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.

Keywords

35J25, 47D07, 47D05, 60J35, 60J60 Boutet de Monvel calculus Feller semigroup Markov process elliptic boundary value problem pseudo-differential operator

Authors and affiliations

  • KazuakiĀ Taira
    • 1
  1. 1.Institute of MathematicsUniversity of TsukubaTsukuba IbarakiJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-43696-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-43695-0
  • Online ISBN 978-3-662-43696-7
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site
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