Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic filtering of a pure jump process with predictable jumps and
  path-dependent local characteristics   The objective of this paper is to study the filtering problem for a system of
partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump
process representing the signal and $Y$ is a general jump-diffusion which
provides observations. Our model covers the case where both processes are not
necessarily quasi left-continuous, allowing them to jump at predictable
stopping times. By introducing the Markovian version of the signal, we are able
to compute an explicit equation for the filtering process via the innovations
approach.

13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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