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Probability Theory and Stochastic Modelling

Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

With Emphasis on the Creation-Annihilation Techniques

Authors: Bouleau, Nicolas, Denis, Laurent

  • Presents a new approach to absolute continuity and regularity of laws of Poisson functionals
  • Richly illustrated by various examples
  • ​Introduces a new mathematical tool, the "lent particle method"  
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eBook 71,39 €
price for France (gross)
  • ISBN 978-3-319-25820-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 89,66 €
price for France (gross)
  • ISBN 978-3-319-25818-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory.

About the authors

Laurent Denis is currently professor at the Université du Maine. He has been head of the department of mathematics at the University of Evry (France). He is a specialist in Malliavin calculus, the theory of stochastic partial differential equations and mathematical finance.

Nicolas Bouleau is emeritus professor at the Ecole des Ponts ParisTech. He is known for his works in potential theory and on Dirichlet forms with which he transformed the approach to error calculus. He has written more than a hundred articles and several books on mathematics and on other subjects related to the philosophy of science. He holds several awards including the Montyon prize from the French Academy of Sciences and is a member of the Scientific Council of the Nicolas Hulot Foundation.

Reviews

“This book is based on a course given at the Institute Henri Poincare in Paris, in 2011. … this is a deep book that is very well written and could be interesting to anybody working with jump diffusion stochastic models.” (Josep Vives, Mathematical Reviews, February, 2017)


Table of contents (10 chapters)

  • Introduction

    Bouleau, Nicolas (et al.)

    Pages 1-8

    Preview Buy Chapter 29,94 €
  • Introduction to the Theory of Dirichlet Forms

    Bouleau, Nicolas (et al.)

    Pages 9-29

    Preview Buy Chapter 29,94 €
  • Reminders on Poisson Random Measures

    Bouleau, Nicolas (et al.)

    Pages 31-39

    Preview Buy Chapter 29,94 €
  • Construction of the Dirichlet Structure on the Upper Space

    Bouleau, Nicolas (et al.)

    Pages 41-81

    Preview Buy Chapter 29,94 €
  • The Lent Particle Formula

    Bouleau, Nicolas (et al.)

    Pages 83-105

    Preview Buy Chapter 29,94 €

Buy this book

eBook 71,39 €
price for France (gross)
  • ISBN 978-3-319-25820-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 89,66 €
price for France (gross)
  • ISBN 978-3-319-25818-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
Book Subtitle
With Emphasis on the Creation-Annihilation Techniques
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
76
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-25820-1
DOI
10.1007/978-3-319-25820-1
Hardcover ISBN
978-3-319-25818-8
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XVIII, 323
Number of Illustrations and Tables
3 illustrations in colour
Topics