Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching processes with pairwise interactions   In this manuscript, we are interested on the long-term behaviour of branching
processes with pairwise interactions (BPI-processes). A process in this class
behaves as a pure branching process with the difference that competition and
cooperation events between pairs of individual are also allowed. BPI-processes
form a subclass of branching processes with interactions, which were recently
introduced by Gonz\'alez Casanova et al. (2017), and includes the so-called
logistic branching process which was studied by Lambert (2005).
  Here, we provide a series of integral tests that fully explains how
competition and cooperation regulates the long-term behaviour of BPI-processes.
In particular, we give necessary and sufficient conditions for the events of
explosion and extinction, as well as conditions under which the process comes
down from infinity. Moreover, we also determine whether the process admits, or
not, a stationary distribution. Our arguments uses the moment dual of
BPI-processes which turns out to be a family of diffusions taking values on
$[0,1]$, that we introduce as generalised Wright-Fisher diffusions together
with a complete understanding of the nature of their boundaries.

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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an