Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizing Dirichlet-to-Neumann operators   The aim of this paper is to study the Dirichlet-to-Neumann operators in the
context of Dirichlet forms and especially to figure out their probabilistic
counterparts. Regarding irreducible Dirichlet forms, we will show that the
Dirichlet-to-Neumann operators for them are associated with the trace Dirichlet
forms corresponding to the time changed processes on the boundary. Furthermore,
the Dirichlet-to-Neumann operators for perturbations of Dirichlet forms will be
also explored. It turns out that for typical cases such a Dirichlet-to-Neumann
operator corresponds to a quasi-regular positivity preserving (symmetric)
coercive form, so that there exists a family of Markov processes associated
with it via Doob's $h$-transformations.

27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci