Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simulation of McKean Vlasov SDEs with super linear growth   We present two fully probabilistic Euler schemes, one explicit and one
implicit, for the simulation of McKean-Vlasov Stochastic Differential Equations
(MV-SDEs) with drifts of super-linear growth and random initial condition.
  We provide a pathwise propagation of chaos result and show strong convergence
for both schemes on the consequent particle system. The explicit scheme attains
the standard $1/2$ rate in stepsize. From a technical point of view, we
successfully use stopping times to prove the convergence of the implicit method
although we avoid them altogether for the explicit one. The combination of
particle interactions and random initial condition makes the proofs technically
more involved.
  Numerical tests recover the theoretical convergence rates and illustrate a
computational complexity advantage of the explicit over the implicit scheme. A
comparative analysis is carried out on a stylized non-Lipschitz MV-SDE and a
mean-field model for FitzHugh-Nagumo neurons. We provide numerical tests
illustrating "particle corruption" effect where one single particle diverging
can "corrupt" the whole particle system. Moreover, the more particles in the
system the more likely this divergence is to occur.

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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas