A semigroup approach to nonlinear Lévy processes - Robert Denk; Michael Kupper; Max Nendel (Bielefeld University, Center for Mathematical Economics (IMW), 2019)
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.
urn:nbn:de:0070-pub-29342305
Keywords: G51; L25; H20; 330; Lévy process; convex expectation space; Markovian convolution semigroup; fully nonlinear PDE; Nisio semigroup