Lecture Notes in Mathematics

Local Times and Excursion Theory for Brownian Motion

A Tale of Wiener and Itô Measures

Authors: Yen, Ju-Yi, Yor, Marc

  • 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
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About this book

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. 

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)


Table of contents (11 chapters)

  • Prerequisites

    Yen, Ju-Yi (et al.)

    Pages 1-10

  • The Existence and Regularity of Semimartingale Local Times

    Yen, Ju-Yi (et al.)

    Pages 13-28

  • Lévy’s Representation of Reflecting BM and Pitman’s Representation of BES(3)

    Yen, Ju-Yi (et al.)

    Pages 29-41

  • Paul Lévy’s Arcsine Laws

    Yen, Ju-Yi (et al.)

    Pages 43-54

  • Brownian Excursion Theory: A First Approach

    Yen, Ju-Yi (et al.)

    Pages 57-64

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-01270-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-01269-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Local Times and Excursion Theory for Brownian Motion
Book Subtitle
A Tale of Wiener and Itô Measures
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2088
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-01270-4
DOI
10.1007/978-3-319-01270-4
Softcover ISBN
978-3-319-01269-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 135
Number of Illustrations and Tables
1 b/w illustrations, 8 illustrations in colour
Topics