Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: And$\hat{o}$-Douglas type characterization of generalized conditional
  expectations, optional projections and predictable projections   Generalized conditional expectations, optional projections and predictable
projections of stochastic processes play important roles in the general theory
of stochastic processes, semimartingale theory and stochastic calculus. They
share some important properties with ordinary conditional expectations. While
the characterization of ordinary conditional expectations has been studied by
several authors, no similar work seems to have been done for these three
concepts. This paper aims at undertaking this task by giving
And$\hat{o}$-Douglas type characterization theorem for each of them.

26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org