Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal approximation of SDEs on submanifolds: the Ito-vector and
  Ito-jet projections   We define two new notions of projection of a stochastic differential equation
(SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows
one to systematically develop low dimensional approximations to high
dimensional SDEs using differential geometric techniques. The approach
generalizes the notion of projecting a vector field onto a submanifold in order
to derive approximations to ordinary differential equations, and improves the
previous Stratonovich projection method by adding optimality analysis and
results. Indeed, just as in the case of ordinary projection, our definitions of
projection are based on optimality arguments and give in a well-defined sense
"optimal" approximations to the original SDE in the mean-square sense. We also
show that the Stratonovich projection satisfies an optimality criterion that is
more ad hoc and less appealing than the criteria satisfied by the Ito
projections we introduce. As an application we consider approximating the
solution of the non-linear filtering problem with a Gaussian distribution and
show how the newly introduced Ito projections lead to optimal approximations in
the Gaussian family and briefly discuss the optimal approximation for more
general families of distribution. We perform a numerical comparison of our
optimally approximated filter with the classical Extended Kalman Filter to
demonstrate the efficacy of the approach.

3
The categories of this paper are: physics
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th