Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of martingale and moderate deviations for a branching random
  walk with a random environment in time   We consider a branching random walk on $\mathbb{R}$ with a stationary and
ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$
be the counting measure of particles of generation $n$ and $\tilde Z_n(t)=\int
e^{tx}Z_n(dx)$ be its Laplace transform. We show the $L^p$ convergence rate and
the uniform convergence of the martingale $\tilde Z_n(t)/\mathbb E[\tilde
Z_n(t)|\xi]$, and establish a moderate deviation principle for the measures
$Z_n$.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom