Reference : Malliavin and Dirichlet structures for independent random variables |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/45748 | |||

Malliavin and Dirichlet structures for independent random variables | |

English | |

Halconruy, Hélène* [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >] | |

Decreusefond, Laurent* [Télécom Paris > LTCI > > Professor] | |

* These authors have contributed equally to this work. | |

Aug-2019 | |

Stochastic Processes and Their Applications | |

Elsevier | |

129 | |

8 | |

2611-2653 | |

Yes (verified by ORBi^{lu}) | |

International | |

0304-4149 | |

1879-209X | |

Amsterdam | |

Netherlands | |

[en] Malliavin calculus ; Stein's method ; Dirichlet forms | |

[en] On any denumerable product of probability spaces, we construct
a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron-Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of U-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions. | |

http://hdl.handle.net/10993/45748 | |

10.1016/j.spa.2018.07.019 | |

https://arxiv.org/abs/1707.07915 |

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