© 2009

Penalising Brownian Paths


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


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.


Bessel process Brownian motion Martingale Martingales Penalisations Probability theory

Authors and affiliations

  1. 1.Inst. Elie CartanUniversité Nancy IVandoeuvre-les-Nancy CXFrance
  2. 2.Labo. Probabilités Université Paris VIParisFrance

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From the reviews: “In this book the authors give a systematic study of penalisation. The book is divided into 5 chapters. … This book is very useful for graduate students and researchers interested in learning penalisations.” (Ren Ming Song, Mathematical Reviews, Issue 2010 e)