Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

With Emphasis on the Creation-Annihilation Techniques

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes by Nicolas Bouleau, Laurent Denis, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Nicolas Bouleau, Laurent Denis ISBN: 9783319258201
Publisher: Springer International Publishing Publication: January 8, 2016
Imprint: Springer Language: English
Author: Nicolas Bouleau, Laurent Denis
ISBN: 9783319258201
Publisher: Springer International Publishing
Publication: January 8, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Targeting Autophagy in Cancer Therapy by Nicolas Bouleau, Laurent Denis
Cover of the book Microbiome and Cancer by Nicolas Bouleau, Laurent Denis
Cover of the book Ethics and Governance of Biomedical Research by Nicolas Bouleau, Laurent Denis
Cover of the book The Benefits of Natural Products for Neurodegenerative Diseases by Nicolas Bouleau, Laurent Denis
Cover of the book Quantitative Modeling of Operational Risk in Finance and Banking Using Possibility Theory by Nicolas Bouleau, Laurent Denis
Cover of the book Dynamical Systems on Networks by Nicolas Bouleau, Laurent Denis
Cover of the book Service Life Prediction of Exterior Plastics by Nicolas Bouleau, Laurent Denis
Cover of the book Metabolic Influences on Risk for Tendon Disorders by Nicolas Bouleau, Laurent Denis
Cover of the book Applied Multidimensional Systems Theory by Nicolas Bouleau, Laurent Denis
Cover of the book Mathematical Models of Viscous Friction by Nicolas Bouleau, Laurent Denis
Cover of the book Language and Cognitive Structures of Emotion by Nicolas Bouleau, Laurent Denis
Cover of the book Stiff Extrusion Briquetting in Metallurgy by Nicolas Bouleau, Laurent Denis
Cover of the book English for Academic Correspondence by Nicolas Bouleau, Laurent Denis
Cover of the book Introduction to Probability with Statistical Applications by Nicolas Bouleau, Laurent Denis
Cover of the book Automatic Control Systems in Biomedical Engineering by Nicolas Bouleau, Laurent Denis
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy