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Estimation of the Hurst and the stability indices of a $H$-self-similar stable process. (arXiv:1506.05593v2 [math.ST] UPDATED)
来源于:arXiv
In this paper we estimate both the Hurst and the stable indices of a
H-self-similar stable process. More precisely, let $X$ be a $H$-sssi
(self-similar stationary increments) symmetric $\alpha$-stable process. The
process $X$ is observed at points $\frac{k}{n}$, $k=0,\ldots,n$. Our estimate
is based on $\beta$-variations with $-\frac{1}{2}<\beta<0$. We obtain
consistent estimators, with rate of convergence, for several classical $H$-sssi
$\alpha$-stable processes (fractional Brownian motion, well-balanced linear
fractional stable motion, Takenaka's processes, L\'evy motion). Moreover, we
obtain asymptotic normality of our estimators for fractional Brownian motion
and L\'evy motion. \end{abstract} {\bf{Keywords:}} H-sssi processes; stable
processes; self-similarity parameter estimator; stability parameter estimator. 查看全文>>