Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit Theorems for Branching Processes with Immigration in a Random
  Environment   We investigate subcritical Galton-Watson branching processes with immigration
in a random environment. Using Goldie's implicit renewal theory we show that
under general Cram\'er condition the stationary distribution has a power law
tail. We determine the tail process of the stationary Markov chain, prove point
process convergence, and convergence of the partial sums. The original
motivation comes from Kesten, Kozlov and Spitzer seminal 1975 paper, which
connects a random walk in a random environment model to a special Galton-Watson
process with immigration in a random environment. We obtain new results even in
this very special setting.

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The categories of this paper are: eess
18
The categories of this paper are: econ
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con