Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A natural extension of Markov processes and applications to singular
  SDEs   We develop a general method for extending Markov processes to a larger state
space such that the added points form a polar set. The so obtained extension is
an improvement on the standard trivial extension in which case the process is
made stuck in the added points, and it renders a new technique of constructing
extended solutions to S(P)DEs from all starting points, in such a way that they
are solutions at least after any strictly positive time. Concretely, we adopt
this strategy to study SDEs with singular coefficients on an infinite
dimensional state space (e.g. SPDEs of evolutionary type), for which one often
encounters the situation where not every point in the space is allowed as an
initial condition. The same can happen when constructing solutions of
martingale problems or Markov processes from (generalized) Dirichlet forms, to
which our new technique also applies.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org