Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Galerkin approximation scheme for the mean correction in a
  mean-reversion stochastic differential equation   This paper is concerned with the following Markovian stochastic differential
equation of mean-reversion type \[ dR_t= (\theta +\sigma \alpha(R_t, t))R_t dt
+\sigma R_t dB_t \] with an initial value $R_0=r_0\in\mathbb{R}$, where
$\theta\in\mathbb{R}$ and $\sigma>0$ are constants, and the mean correction
function $\alpha:\mathbb{R}\times[0,\infty)\to \alpha(x,t)\in\mathbb{R}$ is
twice continuously differentiable in $x$ and continuously differentiable in
$t$. We first derive that under the assumption of path independence of the
density process of Girsanov transformation for the above stochastic
differential equation, the mean correction function $\alpha$ satisfies a
non-linear partial differential equation which is known as the viscous Burgers
equation. We then develop a Galerkin type approximation scheme for the function
$\alpha$ by utilizing truncation of discretised Fourier transformation to the
viscous Burgers equation.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs