Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak convergence and tightness of probability measures in an abstract
  Skorohod space   In this article, we introduce the space $D([0,1];D)$ of functions defined on
$[0,1]$ with values in the Skorohod space $D$, which are right-continuous and
have left limits with respect to the $J_1$ topology. This space is equipped
with the Skorohod-type distance introduced in Whitt (1980). Following the
classical approach of Billingsley (1968, 1999), we give several criteria for
tightness of probability measures on this space, by characterizing the
relatively compact subsets of this space. In particular, one of these criteria
has been used in the recent article Balan and Saidani (2018) for proving the
existence of a $D$-valued $\alpha$-stable L\'evy motion. Finally, we give a
criterion for weak convergence of random elements in $D([0,1];D)$, and a
criterion for the existence of a process with sample paths in $D([0,1];D)$
based on its finite-dimensional distributions.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex