Reference : Contributions to the asymptotic study of Hermite driven processes |

Dissertations and theses : Doctoral thesis | |||

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

http://hdl.handle.net/10993/34790 | |||

Contributions to the asymptotic study of Hermite driven processes | |

English | |

Tran, Thi Thanh Diu [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > > ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit] | |

25-Jan-2018 | |

University of Luxembourg, Luxembourg | |

Docteur en Mathématiques | |

130 | |

Nourdin, Ivan | |

Thalmaier, Anton | |

Peccati, Giovanni | |

Réveillac, Anthony | |

Tudor, Ciprian | |

[en] Non-central limit theorems ; Limit theorems ; Hermite process ; Rosenblatt process ; Hermite Ornstein-Uhlenbeck process ; Multiple Wiener-Itô integrals | |

[en] This thesis consists of two parts.
Part I is an introduction to Hermite processes, Hermite random ﬁelds, Fisher information and to the papers constituting the thesis. More precisely, in Section 1 we introduce Hermite processes in a nutshell, as well as some of its basic properties. It is the necessary background for the articles [a] and [c]. In Section 2 we consider brieﬂy the multiparameter Hermite random ﬁelds and we study some less elementary facts which are used in the article [b]. In section 3, we recall some terminology about Fisher information related to the article [d]. Finally, our articles [a] to [d] are summarised in Section 4. Part II consists of the articles themselves: [a] T.T. Diu Tran (2017): Non-central limit theorem for quadratic functionals of Hermite-driven long memory moving average processes. Stochastic and Dynamics, 18, no. 4. [b] T.T. Diu Tran (2016): Asymptotic behavior for quadratic variations of nonGaussian multiparameter Hermite random ﬁelds. Under revision for Probability and Mathematical Statistics. [c] I. Nourdin, T.T. Diu Tran (2017): Statistical inference for Vasicek-type model driven by Hermite processes. Submitted to Stochastic Process and their Applications. [d] T.T. Diu Tran (2017+): Fisher information and multivariate Fouth Moment Theorem. Main results have already been obtained. It should be submitted soon. | |

University of Luxembourg - UL | |

Researchers | |

http://hdl.handle.net/10993/34790 |

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