Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the study of processes of classes $\sum(H)$ and $\sum_{s}(H)$   In papers by Yor, a remarkable class $(\Sigma)$ of submartingales is
introduced, which, up to technicalities, are submartingales $(X_{t})_{t\geq0}$
whose increasing process is carried by the times $t$ such that $X_{t}=0$. These
submartingales have several applications in stochastic analysis: for example,
the resolution of Skorokhod embedding problem, the study of Brownian local
times and the study of zeros of continuous martingales. The submartingales of
class $(\Sigma)$ have been extensively studied in a series of articles by
Nikeghbali (part of them in collaboration with Najnudel, some others with
Cheridito and Platen). On the other hand, stochastic calculus has been extended
to signed measures by Ruiz de Chavez \cite{chav} and Beghdadi-Sakrani
\cite{sak}. In \cite{f}, the authors of the present paper have extended the
notion of submartingales of class $(\Sigma)$ to the setting of Ruiz de Chavez
\cite{chav} and Beghdadi-Sakrani \cite{sak}, giving two different classes of
stochastic processes named classes $\sum(H)$ and $\sum_{s}(H)$ where from tools
of the theory of stochastic calculus for signed measures, the authors provide
general frameworks and methods for dealing with processes of these classes. In
this work, we first give some formulas of multiplicative decomposition for
processes of these classes. Afterward, we shall establish some representation
results allowing to recover any process of one of these classes from its final
value and the last time it visited the origin.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin