Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of the Exit Time for L\'evy Processes   This paper is concerned with the behaviour of a L\'{e}vy process when it
crosses over a positive level, $u$, starting from 0, both as $u$ becomes large
and as $u$ becomes small. Our main focus is on the time, $\tau_u$, it takes the
process to transit above the level, and in particular, on the {\it stability}
of this passage time; thus, essentially, whether or not $\tau_u$ behaves
linearly as $u\dto 0$ or $u\to\infty$. We also consider conditional stability
of $\tau_u$ when the process drifts to $-\infty$, a.s. This provides
information relevant to quantities associated with the ruin of an insurance
risk process, which we analyse under a Cram\'er condition.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas