Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak order in averaging principle for two-time-scale stochastic partial
  differential equations   This work is devoted to averaging principle of a two-time-scale stochastic
partial differential equation on a bounded interval $[0, l]$, where both the
fast and slow components are directly perturbed by additive noises. Under some
regular conditions on drift coefficients, it is proved that the rate of weak
convergence for the slow variable to the averaged dynamics is of order
$1-\varepsilon$ for arbitrarily small $\varepsilon>0$. The proof is based on an
asymptotic expansion of solutions to Kolmogorov equations associated with the
multiple-time-scale system.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an