Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

With Emphasis on the Creation-Annihilation Techniques

AvNicolas Bouleau,Laurent Denis

Häftad, Engelska, 2019

Del i serien Probability Theory and Stochastic Modelling

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Beskrivning

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. 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.

Produktinformation

Utgivningsdatum:2019-03-21
Mått:155 x 235 x 19 mm
Vikt:522 g
Format:Häftad
Språk:Engelska
Serie:Probability Theory and Stochastic Modelling
Antal sidor:323
Förlag:Springer International Publishing AG
ISBN:9783319798455

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Mer om författaren

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.

Recensioner i media

“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)

Innehållsförteckning

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.- 4.The 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.- 9.Non Poissonian Cases.- A.Error Structures.- B.The Co-Area Formula.- References.