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Contributions to the asymptotic study of Hermite driven processes
Báo cáo viên: Trần Thị Thanh Dịu (University of Jyvaskyla, Finland)

Thời gian: 14h Thứ 5, ngày 2/07/2020

Địa điểm: P507 nhà A6 hoặc online qua link meet.google.com/odg-dijq-dhs

Tóm tắt:Let $(Z_t^{q, H})_{t geq 0}$ denote a Hermite process of order $qgeq 1$ and self-similarity parameter $H in (frac{1}{2},1)$. This process is $H$-selfsimilar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $qgeq 2$.

In the talk, we firstly focus on the asymptotic behaviour for quadratic functionals of Hermite-driven long memory moving average processes. In the non-Gaussian case $(q geq 2)$, it converges in the sense of finite-dimensional distribution to the Rosenblatt process, irrespective of self-similarity parameter. In the Gaussian case $(q=1)$, either central or non-central limit theorems may arise depending on the value of self-similarity parameter.

Secondly, we apply the above results to construct an estimator for the drift parameter of a Vasicek-type model driven by Hermite process $Z^{q,H}$. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations

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