| 书目名称 | Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes |
| 副标题 | With Emphasis on the |
| 编辑 | Nicolas Bouleau,Laurent Denis |
| 视频video | |
| 概述 | 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".Inclu |
| 丛书名称 | Probability Theory and Stochastic Modelling |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Book 2015 |
| 关键词 | 60H07, 60G57, 60G51, 60J45; Dirichlet forms; Lévy processes; Malliavin calculus; lent particle method; ra |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-25820-1 |
| isbn_softcover | 978-3-319-79845-5 |
| isbn_ebook | 978-3-319-25820-1Series ISSN 2199-3130 Series E-ISSN 2199-3149 |
| issn_series | 2199-3130 |
| copyright | Springer International Publishing Switzerland 2015 |
发表于 2025-3-21 18:38:32
