Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the martingale problem for degenerate-parabolic partial differential
  operators with unbounded coefficients and a mimicking theorem for Ito
  processes   Using results from our companion article [arXiv:1112.4824v2] on a Schauder
approach to existence of solutions to a degenerate-parabolic partial
differential equation, we solve three intertwined problems, motivated by
probability theory and mathematical finance, concerning degenerate diffusion
processes. We show that the martingale problem associated with a
degenerate-elliptic differential operator with unbounded, locally Holder
continuous coefficients on a half-space is well-posed in the sense of Stroock
and Varadhan. Second, we prove existence, uniqueness, and the strong Markov
property for weak solutions to a stochastic differential equation with
degenerate diffusion and unbounded coefficients with suitable H\"older
continuity properties. Third, for an Ito process with degenerate diffusion and
unbounded but appropriately regular coefficients, we prove existence of a
strong Markov process, unique in the sense of probability law, whose
one-dimensional marginal probability distributions match those of the given Ito
process.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th