Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermite spectral method to 1D forward Kolmogorov equation and its
  application to nonlinear filtering problems   In this paper, we investigate the Hermite spectral method (HSM) to
numerically solve the forward Kolmogorov equation (FKE). A useful guideline of
choosing the scaling factor of the generalized Hermite functions is given in
this paper. It greatly improves the resolution of HSM. The convergence rate of
HSM to FKE is analyzed in the suitable function space and has been verified by
the numerical simulation. As an important application and our primary
motivation to study the HSM to FKE, we work on the implementation of the
nonlinear filtering (NLF) problem with a real-time algorithm developed in [17].
The HSM to FKE is served as the off-line computation in this algorithm. The
translating factor of the generalized Hermite functions and the moving-window
technique are introduced to deal with the drifting of the posterior conditional
density function of the states in the on-line experiments. Two numerical
experiments of NLF problems are carried out to illustrate the feasibility of
our algorithm. Moreover, our algorithm surpasses the particle filter as a
real-time solver to NLF.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs