A semigroup approach to nonlinear Lévy processes

Robert Denk, Michael Kupper and Max Nendel

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1616-1642

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 (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.

Keywords: Lévy process; Convex expectation space; Markovian convolution semigroup; Fully nonlinear PDE; Nisio semigroup (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1616-1642

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DOI: 10.1016/j.spa.2019.05.009

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