Center for Mathematical Economics Working Papers No. 610
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
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.
Lévy process convex expectation space Markovian convolution semigroup fully nonlinear PDE Nisio semigroup