Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average and deviation for slow-fast stochastic partial differential
  equations   Averaging is an important method to extract effective macroscopic dynamics
from complex systems with slow modes and fast modes. This article derives an
averaged equation for a class of stochastic partial differential equations
without any Lipschitz assumption on the slow modes. The rate of convergence in
probability is obtained as a byproduct. Importantly, the deviation between the
original equation and the averaged equation is also studied. A martingale
approach proves that the deviation is described by a Gaussian process. This
gives an approximation to errors of $\mathcal{O}(\e)$ instead of
$\mathcal{O}(\sqrt{\e})$ attained in previous averaging.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc