Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martingale-type processes indexed by the real line   Some classes of increment martingales, and the corresponding localized
classes, are studied. An increment martingale is indexed by the real line and
its increment processes are martingales. We focus primarily on the behavior as
time goes to minus infinity in relation to the quadratic variation or the
predictable quadratic variation, and we relate the limiting behavior to the
martingale property. Finally, integration with respect to an increment
martingale is studied.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat