Penalising Brownian Paths

  • Bernard Roynette
  • Marc Yor

Part of the Lecture Notes in Mathematics book series (LNM, volume 1969)

Table of contents

  1. Front Matter
    Pages 1-11
  2. Bernard Roynette, Marc Yor
    Pages 1-34
  3. Bernard Roynette, Marc Yor
    Pages 1-31
  4. Bernard Roynette, Marc Yor
    Pages 1-64
  5. Bernard Roynette, Marc Yor
    Pages 1-36
  6. Back Matter
    Pages 1-21

About this book

Introduction

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one.
We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role.
A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.

Keywords

Bessel process Brownian motion Martingale Martingales Penalisations Probability theory

Authors and affiliations

  • Bernard Roynette
    • 1
  • Marc Yor
    • 2
  1. 1.Inst. Elie CartanUniversité Nancy IVandoeuvre-les-Nancy CXFrance
  2. 2.Labo. Probabilités Université Paris VIParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89699-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-89698-2
  • Online ISBN 978-3-540-89699-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book