Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small value probabilities for supercritical branching processes with
  immigration   We consider a supercritical Galton-Watson branching process with immigration.
It is well known that under suitable conditions on the offspring and
immigration distributions, there is a finite, strictly positive limit
${\mathcal{W}}$ for the normalized population size. Small value probabilities
for ${\mathcal{W}}$ are obtained. Precise effects of the balance between
offspring and immigration distributions are characterized.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an