A Semigroup Approach to Nonlinear Lévy Processes

Robert Denk, Michael Kupper and Max Nendel
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Michael Kupper: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University

No 610, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: Lévy process; convex expectation space; Markovian convolution semigroup; fully nonlinear PDE; Nisio semigroup (search for similar items in EconPapers)
Date: 2019-03-08
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:610

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