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Boundary Value Problems and Markov Processes

  • Authors
  • KazuakiĀ Taira

Part of the Lecture Notes in Mathematics book series (LNM, volume 1499)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Kazuaki Taira
    Pages 1-9
  3. Kazuaki Taira
    Pages 10-22
  4. Kazuaki Taira
    Pages 23-40
  5. Kazuaki Taira
    Pages 50-54
  6. Kazuaki Taira
    Pages 55-60
  7. Kazuaki Taira
    Pages 61-69
  8. Kazuaki Taira
    Pages 70-80
  9. Kazuaki Taira
    Pages 81-104
  10. Back Matter
    Pages 112-132

About this book

Introduction

Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis. The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. As an application, one can construct analytic semigroups corresponding to the diffusion phenomenon of a Markovian particle moving continuously in the state space until it "dies", at which time it reaches the set where the absorption phenomenon occurs. A class of initial-boundary value problems for semilinear parabolic differential equations is also considered. This monograph will appeal to both advanced students and researchers as an introduction to the three interrelated subjects in analysis, providing powerful methods for continuing research.

Keywords

Feller semigroup Markov process Power analytic semigroup convergence differential equation elliptic boundary value problem pseudodifferential operator semilinear parabolic equation stochastic calculus

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092029
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54996-3
  • Online ISBN 978-3-540-46635-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
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