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An Introduction to Random Currents and Their Applications

  • Vincenzo¬†Capasso

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Vincenzo Capasso
    Pages 1-2
  3. Vincenzo Capasso
    Pages 3-19
  4. Vincenzo Capasso
    Pages 21-33
  5. Vincenzo Capasso
    Pages 35-43
  6. Vincenzo Capasso
    Pages 45-65
  7. Back Matter
    Pages 67-143

About this book

Introduction

This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book.  Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis.  Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.  


Keywords

theory of currents Geometric Measure Theory linear functionals statistical shape analysis Crystal dislocations Tumor-driven angiogenesis Stochastic Geometry Push-forward of a current Operations on currents Boundary, and Lie derivative of a current Gaussian currents in statistical shape analysis Random currents on Hilbert spaces Gaussian currents Elements of measure theory Fundamentals of Stochastic Processes

Authors and affiliations

  • Vincenzo¬†Capasso
    • 1
  1. 1.ADAMSS (Centre for Advanced Applied Mathematical and Statistical Sciences)Universit√° degli Studi di Milano La StataleMilanoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94577-4
  • Copyright Information The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94576-7
  • Online ISBN 978-3-319-94577-4
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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