Penalising Brownian Paths

1. Front Matter

   Pages 1-11

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2. Introduction

   • Bernard Roynette, Marc Yor

   Pages 1-34

3. Some penalisations of theWiener measure

   • Bernard Roynette, Marc Yor

   Pages 1-31

4. Feynman-Kac penalisations for Brownian motion

   • Bernard Roynette, Marc Yor

   Pages 1-64

5. Penalisations of a Bessel process with dimension d(0 d 2) by a function of the ranked lengths of its excursions

   • Bernard Roynette, Marc Yor

   Pages 1-93

6. A general principle and some questions about penalisations

   • Bernard Roynette, Marc Yor

   Pages 1-36

7. Back Matter

   Pages 1-21

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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

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)

• Inst. Elie Cartan, Université Nancy I, Vandoeuvre-les-Nancy CX, France

  Bernard Roynette

• Labo. Probabilités , Université Paris VI, Paris, France

  Marc Yor

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