Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Denseness of adapted processes among causal couplings   It is well known that any pair of random variables $(X,Y)$ with values in
Polish spaces, provided that $Y$ is nonatomic, can be approximated in joint law
by random variables of the form $(X',Y)$ where $X'$ is $Y$-measurable and $X'
\stackrel{d}{=} X$. This article surveys and extends some recent dynamic
analogues of this result. For example, if $X$ and $Y$ are stochastic processes
in discrete or continuous time, then, under a nonatomic assumption as well as a
necessary and sufficient causality (or compatibility) condition, one can
approximate $(X,Y)$ in law in path space by processes of the form $(X',Y)$,
where $X'$ is adapted to the filtration generated by $Y$. In addition, in
finite discrete time, we can take $X'$ to have the same law as $X$. A similar
approximation is valid for randomized stopping times, without the first
marginal fixed. Natural applications include relaxations of (mean field)
stochastic control and causal optimal transport problems as well as new
characterizations of the immersion property for progressively enlarged
filtrations.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org