Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discretizing the fractional Levy area   In this article, we give sharp bounds for the Euler- and trapezoidal
discretization of the Levy area associated to a d-dimensional fractional
Brownian motion. We show that there are three different regimes for the exact
root mean-square convergence rate of the Euler scheme. For H<3/4 the exact
convergence rate is n^{-2H+1/2}, where n denotes the number of the
discretization subintervals, while for H=3/4 it is n^{-1} (log(n))^{1/2} and
for H>3/4 the exact rate is n^{-1}. Moreover, the trapezoidal scheme has exact
convergence rate n^{-2H+1/2} for H>1/2. Finally, we also derive the asymptotic
error distribution of the Euler scheme. For H lesser than 3/4 one obtains a
Gaussian limit, while for H>3/4 the limit distribution is of Rosenblatt type.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: eess