Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some aspects of fluctuations of random walks on R and applications to
  random walks on R+ with non-elastic reflection at 0   In this article we refine well-known results concerning the fluctuations of
one-dimensional random walks. More precisely, if $(S_n)_{n \geq 0}$ is a random
walk starting from 0 and $r\geq 0$, we obtain the precise asymptotic behavior
as $n\to\infty$ of $\mathbb P[\tau^{>r}=n, S_n\in K]$ and $\mathbb
P[\tau^{>r}>n, S_n\in K]$, where $\tau^{>r}$ is the first time that the random
walk reaches the set $]r,\infty[$, and $K$ is a compact set. Our assumptions on
the jumps of the random walks are optimal. Our results give an answer to a
question of Lalley stated in [9], and are applied to obtain the asymptotic
behavior of the return probabilities for random walks on $\mathbb R^+$ with
non-elastic reflection at 0.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th