Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A multispecies birth-death-immigration process and its diffusion
  approximation   We consider an extended birth-death-immigration process defined on a lattice
formed by the integers of $d$ semiaxes joined at the origin. When the process
reaches the origin, then it may jumps toward any semiaxis with the same rate.
The dynamics on each ray evolves according to a one-dimensional linear
birth-death process with immigration. We investigate the transient and
asymptotic behavior of the process via its probability generating function. The
stationary distribution, when existing, is a zero-modified negative binomial
distribution. We also study a diffusive approximation of the process, which
involves a diffusion process with linear drift and infinitesimal variance on
each ray. It possesses a gamma-type transient density admitting a stationary
limit.
  As a byproduct of our study, we obtain a closed form of the number of
permutations with a fixed number of components, and a new series form of the
polylogarithm function expressed in terms of the Gauss hypergeometric function.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat