@article{Denk2020semig-40474.2,
  year={2020},
  doi={10.1016/j.spa.2019.05.009},
  title={A semigroup approach to nonlinear Lévy processes},
  number={3},
  volume={130},
  issn={0304-4149},
  journal={Stochastic Processes and their Applications},
  pages={1616--1642},
  author={Denk, Robert and Kupper, Michael and Nendel, Max}
}

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    <dcterms:abstract xml:lang="eng">We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators (Aλ)λ∈Λ of linear Lévy processes which guarantees the existence of a nonlinear Lévy process such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE ∂tu=supλ∈ΛAλu . The results are illustrated with several examples.</dcterms:abstract>
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    <dc:contributor>Kupper, Michael</dc:contributor>
    <dc:contributor>Denk, Robert</dc:contributor>
    <dcterms:title>A semigroup approach to nonlinear Lévy processes</dcterms:title>
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    <dc:contributor>Nendel, Max</dc:contributor>
    <dc:creator>Kupper, Michael</dc:creator>
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