Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity conditions in the realisability problem with applications to
  point processes and random closed sets   We study existence of random elements with partially specified distributions.
The technique relies on the existence of a positive extension for linear
functionals accompanied by additional conditions that ensure the regularity of
the extension needed for interpreting it as a probability measure. It is shown
in which case the extension can be chosen to possess some invariance
properties. The results are applied to the existence of point processes with
given correlation measure and random closed sets with given two-point covering
function or contact distribution function. It is shown that the regularity
condition can be efficiently checked in many cases in order to ensure that the
obtained point processes are indeed locally finite and random sets have closed
realisations.

0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg