Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic control on networks: weak DPP, and verification theorem   The purpose of this article is to study a stochastic control problem on a
junction, with control at the junction point. The problem of control is
formulated in the weak sense, using a relaxed control, namely a control which
takes values in the space of probability measures on a compact set. We prove
first the compactness of the admissible rules and the dynamic programming
principle (DPP). We complete this article by giving a verification Theorem for
the value function of the problem, using some recent results on quasi linear
non degenerate PDE posed on a junction, with non linear Neumann boundary
condition at the junction point. An example is given, where the optimal control
at the junction point is solution of a convex quadratic optimization problem
with linear constraints.

25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg