Dirichlet Forms Methods for Poisson Point Measures and Levy Processes

Name: Dirichlet Forms Methods for Poisson Point Measures and Levy Processes
Brand: Springer International Publishing AG
SKU: 9783319258188
Price: 551.8 PLN
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With Emphasis on the Creation-Annihilation Techniques

Autor: Nicolas Bouleau, Laurent Denis

Język:

Oprawa: Twarda

Wydawca: Springer International Publishing AG

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A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and appl...

Informacje o książce

Autor

Nicolas Bouleau, Laurent Denis

Język

Angielski

Oprawa

Książka - Twarda

Data wydania

2015

strony

323

EAN

9783319258188

ISBN

3319258184

Enbook ID

09545779

Wydawca

Springer International Publishing AG

Waga

674

Wymiary

162 x 243 x 25

Pełny opis

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.

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Dirichlet Forms Methods for Poisson Point Measures and Levy Processes

With Emphasis on the Creation-Annihilation Techniques

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