Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance principles for local times at the supremum of random walks
  and L\'evy processes   We prove that when a sequence of L\'evy processes $X^{(n)}$ or a normed
sequence of random walks $S^{(n)}$ converges a.s. on the Skorokhod space toward
a L\'evy process $X$, the sequence $L^{(n)}$ of local times at the supremum of
$X^{(n)}$ converges uniformly on compact sets in probability toward the local
time at the supremum of $X$. A consequence of this result is that the sequence
of (quadrivariate) ladder processes (both ascending and descending) converges
jointly in law towards the ladder processes of $X$. As an application, we show
that in general, the sequence $S^{(n)}$ conditioned to stay positive converges
weakly, jointly with its local time at the future minimum, towards the
corresponding functional for the limiting process $X$. From this we deduce an
invariance principle for the meander which extends known results for the case
of attraction to a stable law.

36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga