TY  - GEN
AB  - 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.
DA  - 2019
KW  - Lévy process
KW  - convex expectation space
KW  - Markovian convolution semigroup
KW  - fully nonlinear PDE
KW  - Nisio semigroup
LA  - eng
PY  - 2019
SN  - 0931-6558
TI  - A Semigroup Approach to Nonlinear Lévy Processes
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29342305
Y2  - 2024-11-24T12:41:00
ER  -