Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Berry-Ess\'een bounds for the least squares estimator for discretely
  observed fractional Ornstein-Uhlenbeck processes   Let $\theta>0$. We consider a one-dimensional fractional Ornstein-Uhlenbeck
process defined as $dX_t= -\theta\ X_t dt+dB_t,\quad t\geq0,$ where $B$ is a
fractional Brownian motion of Hurst parameter $H\in(1/2,1)$. We are interested
in the problem of estimating the unknown parameter $\theta$. For that purpose,
we dispose of a discretized trajectory, observed at $n$ equidistant times
$t_i=i\Delta_{n}, i=0,...,n$, and $T_n=n\Delta_{n}$ denotes the length of the
`observation window'. We assume that $\Delta_{n} \rightarrow 0$ and
$T_n\rightarrow \infty$ as $n\rightarrow \infty$. As an estimator of $\theta$
we choose the least squares estimator (LSE) $\hat{\theta}_{n}$. The consistency
of this estimator is established. Explicit bounds for the Kolmogorov distance,
in the case when $H\in(1/2,3/4)$, in the central limit theorem for the LSE
$\hat{\theta}_{n}$ are obtained. These results hold without any kind of
ergodicity on the process $X$.

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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg