Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal transport bounds between the time-marginals of a
  multidimensional diffusion and its Euler scheme   In this paper, we prove that the time supremum of the Wasserstein distance
between the time-marginals of a uniformly elliptic multidimensional diffusion
with coefficients bounded together with their derivatives up to the order $2$
in the spatial variables and H{\"o}lder continuous with exponent $\gamma$ with
respect to the time variable and its Euler scheme with $N$ uniform time-steps
is smaller than $C \left(1+\mathbf{1}\_{\gamma=1}
\sqrt{\ln(N)}\right)N^{-\gamma}$. To do so, we use the theory of optimal
transport. More precisely, we investigate how to apply the theory by Ambrosio,
Gigli and Savar{\'e} to compute the time derivative of the Wasserstein distance
between the time-marginals. We deduce a stability inequality for the
Wasserstein distance which finally leads to the desired estimation.

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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an