Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semigroup approach to nonlinear L\'evy processes   We study the relation between L\'evy processes under nonlinear expectations,
nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one
relation between nonlinear L\'evy processes and nonlinear Markovian convolution
semigroups. Second, we provide a condition on a family of infinitesimal
generators $(A_\lambda)_{\lambda\in\Lambda}$ of linear L\'evy processes which
guarantees the existence of a nonlinear L\'evy processes such that the
corresponding nonlinear Markovian convolution semigroup is a viscosity solution
of the fully nonlinear PDE $\partial_t u=\sup_{\lambda\in \Lambda} A_\lambda
u$. The results are illustrated with several examples.

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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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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: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: cs