Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solutions of Kolmogorov's equations for jump Markov processes   This paper studies three ways to construct a nonhomogeneous jump Markov
process: (i) via a compensator of the random measure of a multivariate point
process, (ii) as a minimal solution of the backward Kolmogorov equation, and
(iii) as a minimal solution of the forward Kolmogorov equation. The main
conclusion of this paper is that, for a given measurable transition intensity,
commonly called a Q-function, all these constructions define the same
transition function. If this transition function is regular, that is, the
probability of accumulation of jumps is zero, then this transition function is
the unique solution of the backward and forward Kolmogorov equations. For
continuous Q-functions, Kolmogorov equations were studied in Feller's seminal
paper. In particular, this paper extends Feller's results for continuous
Q-functions to measurable Q-functions and provides additional results.

36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys