Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renewal theory for iterated perturbed random walks on a general
  branching process tree: intermediate generations   Let $(\xi_k,\eta_k)_{k\in\mathbb{N}}$ be independent identically distributed
random vectors with arbitrarily dependent positive components. We call a
(globally) perturbed random walk a random sequence $(T_k)_{k\in\mathbb{N}}$
defined by $T_k:=\xi_1+\cdots+\xi_{k-1}+\eta_k$ for $k\in\mathbb{N}$. Further,
by an iterated perturbed random walk is meant the sequence of point processes
defining the birth times of individuals in subsequent generations of a general
branching process provided that the birth times of the first generation
individuals are given by a perturbed random walk. For $j\in\mathbb{N}$ and
$t\geq 0$, denote by $N_j(t)$ the number of the $j$th generation individuals
with birth times $\leq t$. In this article we prove counterparts of the
classical renewal-theoretic results (the elementary renewal theorem,
Blackwell's theorem and the key renewal theorem) for $N_j(t)$ under the
assumption that $j=j(t)\to\infty$ and $j(t)=o(t^{2/3})$ as $t\to\infty$.
According to our terminology, such generations form a subset of the set of
intermediate generations.

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The categories of this paper are: stat
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph