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Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection

  • Book
  • © 2014

Overview

Authors:
  1. Benedict Baur

    1. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

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  • Publication in the field of mathematical sciences
  • Includes supplementary material: sn.pub/extras

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Benedict Baur
    Pages 1-8

  3. Construction of \({L^p}\)-Strong Feller Processes

    • Benedict Baur
    Pages 9-41

  4. Elliptic Regularity up to the Boundary

    • Benedict Baur
    Pages 43-54

  5. Construction of Elliptic Diffusions

    • Benedict Baur
    Pages 55-70

  6. Applications

    • Benedict Baur
    Pages 71-81

  7. Construction of the Local Time and Skorokhod Decomposition

    • Benedict Baur
    Pages 83-127

  8. Appendix

    • Benedict Baur
    Pages 129-187

  9. Back Matter

    Pages 189-198
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Keywords

About this book

Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods, regularity for solutions of elliptic boundary value problems, construction of elliptic diffusions with singular drift and reflection, Skorokhod decomposition and applications to Mathematical Physics like finite particle systems with singular interaction. Emphasize is placed on the handling of singular drift coefficients, as well as on the discussion of point wise and path wise properties of the constructed processes rather than just the quasi-everywhere properties commonly known from the general Dirichlet form theory.

Reviews

“The author presents modern functional analytic methods for the construction and analysis of Feller processes in general and diffusion processes in particular. … This book is a must-read for people who are interested in (stochastic) differential equations, Dirichlet forms, stochastic processes and their applications.” (J. A. Van Casteren, Mathematical Reviews, November, 2015)

Authors and Affiliations

  • Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Benedict Baur

About the author

Benedict Baur has done his doctor’s degree at the University of Kaiserslautern in topics on Stochastics and Functional Analysis.

Bibliographic Information

  • Book Title: Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection

  • Authors: Benedict Baur

  • DOI: https://doi.org/10.1007/978-3-658-05829-6

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2014

  • Softcover ISBN: 978-3-658-05828-9Published: 08 May 2014

  • eBook ISBN: 978-3-658-05829-6Published: 25 April 2014

  • Edition Number: 1

  • Number of Pages: X, 198

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis, Probability Theory and Stochastic Processes, Mathematical Physics

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