Dirichlet Forms Methods for Poisson Point ...

Dekorationsartikel gehören nicht zum Leistungsumfang.

Sprache: Englisch

123,95 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 1-2 Wochen

Kategorien:

Der Artikel ist nicht in deutscher Sprache verfasst.
Die Sprache der Produktbeschreibung und Details kann in Englisch angegeben sein. Sollten Sie Verständnisprobleme haben, wenden Sie sich gerne an uns.

Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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"

Includes supplementary material: [...]

Inhaltsverzeichnis

Introduction.- Notations and Basic Analytical Properties.- 1.Reminders on Poisson Random Measures, Lévy Processes and Dirichlet Forms.- 2.Dirichlet Forms and (EID).- 3.Construction of the Dirichlet Structure on the Upper Space.- [...] Lent Particle Formula and Related Formulae.- 5.Sobolev Spaces and Distributions on Poisson Space.- 6.- Space-Time Setting and Processes.- 7.Applications to Stochastic Differential Equations driven by a Random Measure.- 8.Affine Processes, Rates Models.- [...] Poissonian Cases.- [...] Structures.- [...] Co-Area Formula.- References.

Details

Erscheinungsjahr:	2015
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xviii 323 S. 3 farbige Illustr. 323 p. 3 illus. in color.
ISBN-13:	9783319258188
ISBN-10:	3319258184
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Denis, Laurent Bouleau, Nicolas
Auflage:	1st ed. 2015
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Probability Theory and Stochastic Modelling
Maße:	241 x 160 x 25 mm
Von/Mit:	Laurent Denis (u. a.)
Erscheinungsdatum:	23.12.2015
Gewicht:	0,682 kg

Artikel-ID: 104209308