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  • © 2014

Semigroups, Boundary Value Problems and Markov Processes

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  • Includes four new chapters and eight re-worked and expanded chapters
  • Notes and comments where bibliographical references are discussed, are inserted in all chapters
  • New references have been added to the bibliography

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xix
  2. Introduction and Main Results

    • Kazuaki Taira
    Pages 1-31
  3. Elements of Analysis

    1. Front Matter

      Pages 33-33
    2. Elements of Probability Theory

      • Kazuaki Taira
      Pages 35-98
    3. Elements of Functional Analysis

      • Kazuaki Taira
      Pages 99-142
    4. Theory of Semigroups

      • Kazuaki Taira
      Pages 143-198
  4. Elements of Partial Differential Equations

    1. Front Matter

      Pages 199-199
    2. Theory of Distributions

      • Kazuaki Taira
      Pages 201-283
    3. Sobolev and Besov Spaces

      • Kazuaki Taira
      Pages 285-311
    4. Theory of Pseudo-differential Operators

      • Kazuaki Taira
      Pages 313-360
    5. Waldenfels Operators and Maximum Principles

      • Kazuaki Taira
      Pages 361-408
  5. Markov Processes, Semigroups and Boundary Value Problems

    1. Front Matter

      Pages 409-409
    2. Proof of Theorem 1.3

      • Kazuaki Taira
      Pages 547-561
    3. Markov Processes Revisited

      • Kazuaki Taira
      Pages 563-589
    4. Concluding Remarks

      • Kazuaki Taira
      Pages 591-604
  6. Back Matter

    Pages 605-716

About this book

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.

Authors and Affiliations

  • Institute of Mathematics, University of Tsukuba, Tsukuba Ibaraki, Japan

    Kazuaki Taira

About the author

Professor Kazuaki TAIRA, born in Tokyo, Japan in 1946, served for many years as a Professor of Mathematics at the University of Tsukuba (1998-2009). He received his Bachelor of Science in 1969 from the University of Tokyo, Japan and his Master of Science in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 to 1978. The Doctor of Science degree was awarded to him in 1976 by the University of Tokyo and in 1978 the Doctorat d'Etat degree was given to him by Universite de Paris-Sud, France. He held a French government scholarship from 1976 to 1978.

He has also served as a member of the Institute for Advanced Study, USA (1980-1981), as an Associate Professor at the University of Tsukuba (1981-1995) and as a Professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted an invitation from the University of Tsukuba to teach there again as a Professor. Since 2009, he has also been a part-time Professor at Waseda University. His current research interests are in the study of three interrelated subjects in analysis: semi groups, elliptic boundary value problems and Markov processes.

Bibliographic Information

Buy it now

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access