Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean field limits for interacting Hawkes processes in a diffusive regime   We consider a sequence of systems of Hawkes processes having mean field
interactions in a diffusive regime. The stochastic intensity of each process is
a solution of a stochastic differential equation driven by N independent
Poisson random measures. We show that, as the number of interacting components
N tends to infinity, this intensity converges in distribution in Skorohod space
to a CIR-type diffusion. Moreover, we prove the convergence in distribution of
the Hawkes processes to the limit point process having the limit diffusion as
intensity. To prove the convergence results, we use analytical technics based
on the convergence of the associated infinitesimal generators and Markovian
semigroups.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat