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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes: With Emphasis on the Creation-Annihilation Techniques: 76 (Probability Theory and Stochastic Modelling) - Softcover
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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.
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Über die Autorin bzw. 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.
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes : With Emphasis on the Creation-annihilation Techniques
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Dirichlet Forms Methods for Poisson Point Measures and Lvy Processes (Paperback)
Verlag:
Springer International Publishing AG, Cham, 2019
ISBN 10: 3319798456
ISBN 13: 9783319798455
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Paperback. Zustand: new. Paperback. 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 Levy 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9783319798455
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes: With Emphasis on the Creation-Annihilation Techniques (Probability Theory and Stochastic Modelling, 76)
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes: With Emphasis on the Creation-Annihilation Techniques (Probability Theory and Stochastic Modelling, 76)
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes : With Emphasis on the Creation-annihilation Techniques
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes: With Emphasis on the Creation-Annihilation Techniques (Probability Theory and Stochastic Modelling, 76)
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
Verlag:
Springer International Publishing Mrz 2019, 2019
ISBN 10: 3319798456
ISBN 13: 9783319798455
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Taschenbuch
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 344 pp. Englisch. Bestandsnummer des Verkäufers 9783319798455
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Dirichlet Forms Methods for Poisson Point Measures and L?vy Processes: With Emphasis on the Creation-Annihilation Techniques (Probability Theory and Stochastic Modelling (76))
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Dirichlet Forms Methods for Poisson Point Measures and L?vy Processes: With Emphasis on the Creation-Annihilation Techniques
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Dirichlet Forms Methods for Poisson Point Measures and L?vy Processes: With Emphasis on the Creation-Annihilation Techniques (Probability Theory and Stochastic Modelling (76))
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