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© 2013

Local Times and Excursion Theory for Brownian Motion

A Tale of Wiener and Itô Measures

Benefits

  • Both local times and excursion theory are usually discussed in much longer texts. We examine these topics in relation to readers’ basic knowledge of stochastic processes

  • Presents interesting applications of excursion theory

  • Similarly with local times of Brownian motion

Book

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

  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Labo. Probabilités et Modèles AléatoiresUniversité Paris VI CNRS UMR 7599Paris CX 05France

Bibliographic information

  • Book Title Local Times and Excursion Theory for Brownian Motion
  • Book Subtitle A Tale of Wiener and Itô Measures
  • Authors Ju-Yi Yen
    Marc Yor
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-01269-8
  • eBook ISBN 978-3-319-01270-4
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages IX, 135
  • Number of Illustrations 1 b/w illustrations, 8 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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Reviews

“The lecture notes provide an elementary and brief introduction to local times for continuous semimartingales and excursion theory for Brownian motion. … The lecture notes are an easily accessible and self-contained introduction … which are suitable for graduate students with a basic knowledge of stochastic processes in continuous time. … the proofs are mostly carried out with many details and helpful references are given in each chapter.” (David Prömel, zbMATH 1364.60003, 2017)