Local Times and Excursion Theory for Brownian Motion

A Tale of Wiener and Itô Measures

  • Ju-Yi Yen
  • Marc Yor

Part of the Lecture Notes in Mathematics book series (LNM, volume 2088)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ju-Yi Yen, Marc Yor
    Pages 1-10
  3. Local Times of Continuous Semimartingales

    1. Front Matter
      Pages 11-11
    2. Ju-Yi Yen, Marc Yor
      Pages 43-54
  4. Excursion Theory for Brownian Paths

    1. Front Matter
      Pages 55-55
    2. Ju-Yi Yen, Marc Yor
      Pages 57-64
    3. Ju-Yi Yen, Marc Yor
      Pages 65-77
    4. Ju-Yi Yen, Marc Yor
      Pages 101-104
  5. Some Applications of Excursion Theory

    1. Front Matter
      Pages 105-105
    2. Ju-Yi Yen, Marc Yor
      Pages 107-110
    3. Ju-Yi Yen, Marc Yor
      Pages 111-131
  6. Back Matter
    Pages 133-138

About this book

Introduction

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.

Keywords

arcsine law excursion theory functionals of Brownian motion local times

Authors and affiliations

  • Ju-Yi Yen
    • 1
  • Marc Yor
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Labo. Probabilités et Modèles AléatoiresUniversité Paris VI CNRS UMR 7599Paris CX 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01270-4
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-01269-8
  • Online ISBN 978-3-319-01270-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book