Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluid approach to two-sided Markov-modulated Brownian motion   We extend to Markov-modulated Brownian motion (MMBM) the renewal approach
which has been successfully applied to the analysis of Markov-modulated fluid
models. It has recently been shown that MMBM may be expressed as the limit of a
parameterized family of Markov-modulated fluid models. We prove that the weak
convergence also holds for systems with two reflecting boundaries, one at zero
and one at $b >0$, and that the stationary distributions of the approximating
fluid models converge to the stationary distribution of the two-sided reflected
MMBM. Thus, we obtain a new representation for the stationary distribution,
effectively separating the limiting behaviour of the process at the boundaries
from its behaviour in the interior of $(0,b)$.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph