Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Qualitative properties of certain piecewise deterministic Markov
  processes   We study a class of Piecewise Deterministic Markov Processes with state space
Rd x E where E is a finite set. The continuous component evolves according to a
smooth vector field that is switched at the jump times of the discrete
coordinate. The jump rates may depend on the whole position of the process.
Working under the general assumption that the process stays in a compact set,
we detail a possible construction of the process and characterize its support,
in terms of the solutions set of a differential inclusion. We establish results
on the long time behaviour of the process, in relation to a certain set of
accessible points, which is shown to be strongly linked to the support of
invariant measures. Under H\"ormander-type bracket conditions, we prove that
there exists a unique invariant measure and that the processes converges to
equilibrium in total variation. Finally we give examples where the bracket
condition does not hold, and where there may be one or many invariant measures,
depending on the jump rates between the flows.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph