Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martin Boundary and Integral Representation for Harmonic Functions of
  Symmetric Stable Processes   Martin boundaries and integral representations of positive functions which
are harmonic in a bounded domain $D$ with respect to Brownian motion are well
understood. Unlike the Brownian case, there are two different kinds of
harmonicity with respect to a discontinuous symmetric stable process. One kind
are functions harmonic in $D$ with respect to the whole process $X$, and the
other are functions harmonic in $D$ with respect to the process $X^D$ killed
upon leaving $D$. In this paper we show that for bounded Lipschitz domains, the
Martin boundary with respect to the killed stable process $X^D$ can be
identified with the Euclidean boundary. We further give integral
representations for both kinds of positive harmonic functions. Also given is
the conditional gauge theorem conditioned according to Martin kernels and the
limiting behaviors of the $h$-conditional stable process, where $h$ is a
positive harmonic function of $X^D$. In the case when $D$ is a bounded $C^{1,
1}$ domain, sharp estimate on the Martin kernel of $D$ is obtained.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph