Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional limit theorems for random walks perturbed by positive
  alpha-stable jumps   Let $\xi_1$, $\xi_2,\ldots$ be i.i.d. random variables of zero mean and
finite variance and $\eta_1$, $\eta_2,\ldots$ positive i.i.d. random variables
whose distribution belongs to the domain of attraction of an $\alpha$-stable
distribution, $\alpha\in (0,1)$. The two collections are assumed independent.
We consider a Markov chain with jumps of two types. If the present position of
the Markov chain is positive, then the jump $\xi_k$ occurs; if the present
position of the Markov chain is nonpositive, then its next position is
$\eta_j$. We prove a functional limit theorem for this Markov chain under
Donsker's scaling. The weak limit is a nonnegative process $(X(t))_{t\geq 0}$
satisfying a stochastic equation ${\rm d}X(t)={\rm d}W(t)+ {\rm
d}U_\alpha(L_X^{(0)}(t))$, where $W$ is a Brownian motion, $U_\alpha$ is an
$\alpha$-stable subordinator which is independent of $W$, and $L_X^{(0)}$ is a
local time of $X$ at $0$. Also, we explain that $X$ is a Feller Brownian motion
with a `jump-type' exit from $0$.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an