Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong solutions and strong Feller properties for regime-switching
  diffusion processes in an infinite state space   We establish the existence and pathwise uniqueness of regime-switching
diffusion processes in an infinite state space, which could be
time-inhomogeneous and state-dependent. Then the strong Feller properties of
these processes are investigated by using the theory of parabolic differential
equations and dimensional-free Harnack inequalities.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat