Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ninomiya-Victoir scheme: strong convergence, antithetic version and
  application to multilevel estimators   In this paper, we are interested in the strong convergence properties of the
Ninomiya-Victoir scheme which is known to exhibit weak convergence with order
2. We prove strong convergence with order $1/2$. This study is aimed at
analysing the use of this scheme either at each level or only at the finest
level of a multilevel Monte Carlo estimator: indeed, the variance of a
multilevel Monte Carlo estimator is related to the strong error between the two
schemes used on the coarse and fine grids at each level. Recently, Giles and
Szpruch proposed a scheme permitting to construct a multilevel Monte Carlo
estimator achieving the optimal complexity $O\left(\epsilon^{-2}\right)$ for
the precision $\epsilon$. In the same spirit, we propose a modified
Ninomiya-Victoir scheme, which may be strongly coupled with order $1$ to the
Giles-Szpruch scheme at the finest level of a multilevel Monte Carlo estimator.
Numerical experiments show that this choice improves the efficiency, since the
order $2$ of weak convergence of the Ninomiya-Victoir scheme permits to reduce
the number of discretization levels.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph