# A Semigroup Approach to Nonlinear Lévy Processes

Denk R, Kupper M, Nendel M (2019) Center for Mathematical Economics Working Papers; 610.
Bielefeld: Center for Mathematical Economics.

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Diskussionspapier | Veröffentlicht | Englisch
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Abstract / Bemerkung
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 ($A_\lambda$) $_{\lambda\in \Lambda}$ 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 $\partial_t u=\sup_{\lambda\in \Lambda} A_\lambda u$. The results are illustrated with several examples.
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610
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Denk R, Kupper M, Nendel M. A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers. Vol 610. Bielefeld: Center for Mathematical Economics; 2019.
Denk, R., Kupper, M., & Nendel, M. (2019). A Semigroup Approach to Nonlinear Lévy Processes (Center for Mathematical Economics Working Papers, 610). Bielefeld: Center for Mathematical Economics.
Denk, R., Kupper, M., and Nendel, M. (2019). A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers, 610, Bielefeld: Center for Mathematical Economics.
Denk, R., Kupper, M., & Nendel, M., 2019. A Semigroup Approach to Nonlinear Lévy Processes, Center for Mathematical Economics Working Papers, no.610, Bielefeld: Center for Mathematical Economics.
R. Denk, M. Kupper, and M. Nendel, A Semigroup Approach to Nonlinear Lévy Processes, Center for Mathematical Economics Working Papers, vol. 610, Bielefeld: Center for Mathematical Economics, 2019.
Denk, R., Kupper, M., Nendel, M.: A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers, 610. Center for Mathematical Economics, Bielefeld (2019).
Denk, Robert, Kupper, Michael, and Nendel, Max. A Semigroup Approach to Nonlinear Lévy Processes. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 610.
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