Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak backward error analysis for SDEs   We consider numerical approximations of stochastic differential equations by
the Euler method. In the case where the SDE is elliptic or hypoelliptic, we
show a weak backward error analysis result in the sense that the generator
associated with the numerical solution coincides with the solution of a
modified Kolmogorov equation up to high order terms with respect to the
stepsize. This implies that every invariant measure of the numerical scheme is
close to a modified invariant measure obtained by asymptotic expansion.
Moreover, we prove that, up to negligible terms, the dynamic associated with
the Euler scheme is exponentially mixing.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph