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- W2779341337 abstract "Let $Z$ denote a Hermite process of order $q geq 1$ and self-similarity parameter $H in (frac{1}{2}, 1)$. This process is $H$-self-similar, 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 this paper, we deal with a Vasicek-type model driven by $Z$, of the form $dX_t = a(b - X_t)dt +dZ_t$. Here, $a > 0$ and $b in mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations." @default.
- W2779341337 created "2018-01-05" @default.
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- W2779341337 date "2017-12-16" @default.
- W2779341337 modified "2023-09-27" @default.
- W2779341337 title "Statistical inference for Vasicek-type model driven by Hermite processes" @default.
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