Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
Language: English
Published by Springer International Publishing AG, CH, 2015
Series: Book 8 of 35 - Probability Theory and Stochastic Modelling
- Hardcover
- New
Seller: Rarewaves.com USA, London, London, United KingdomRarewaves.com USA
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Condition: New
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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.…
Seller Inventory # LU-9783319258188
- Title
- Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
- Author
- Nicolas Bouleau, Laurent Denis
- Publisher
- Springer International Publishing AG, CH
- Publication year
- 2015
- Condition
- New
- Binding
- Hardback
- Language
- English
- ISBN 10
- 3319258184
- ISBN 13
- 9783319258188
- Edition
- 1st ed. 2015.
- Series
- Book 8 of 35: Probability Theory and Stochastic Modelling
"Synopsis" may belong to another edition of this title.
About the Author
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.
"About the title" may belong to another edition of this title.
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