Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic moments and large deviations for a critical Galton-Watson
  process with immigration   In this paper, a critical Galton-Watson branching process with immigration
$Z_{n}$ is studied. We first obtain the convergence rate of the harmonic moment
of $Z_{n}$. Then the large deviation of $S_{Z_n}:=\sum_{i=1}^{Z_n} X_i$ is
obtained, where $\{X_i\}$ is a sequence of independent and identically
distributed zero-mean random variables with tail index $\alpha>2$. We shall see
that the converging rate is determined by the immigration mean, the variance of
reproducing and the tail index of $X_1^+$, comparing to previous result for
supercritical case, where the rate depends on the Schr\"{o}der constant and the
tail index.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga