Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional limit theorem for locally perturbed random walks   A particle moves randomly over the integer points of the real line. Jumps of
the particle outside the membrane (a fixed "locally perturbating set") are
i.i.d., have zero mean and finite variance, whereas jumps of the particle from
the membrane have other distributions with finite means which may be different
for different points of the membrane; furthermore, these jumps are mutually
independent and independent of the jumps outside the membrane. Assuming that
the particle cannot jump over the membrane we prove that the weak scaling limit
of the particle position is a skew Brownian motion with parameter $\gamma\in
[-1,1]$. The path of a skew Brownian motion is obtained by taking each
excursion of a reflected Brownian motion, independently of the others, positive
with probability $2^{-1}(1+\gamma)$ and negative with probability
$2^{-1}(1-\gamma)$. To prove the weak convergence result we offer a new
approach which is based on the martingale characterization of a skew Brownian
motion. Among others, this enables us to provide the explicit formula for the
parameter $\gamma$. In the previous articles the explicit formulae for the
parameter have only been obtained under the assumption that outside the
membrane the particle performs unit jumps.

23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex