Nonlinear Lévy processes and their characteristics (Q2826754)

Nonlinear Lévy processes were introduced by \textit{M. Hu} and \textit{S. Peng} in [``G-Lévy processes under sublinear expectations'', Preprint, \url{arXiv:0911.3533}]. Extending their work, the authors of the current paper construct a sublinear expectation on the Skorokhod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of Lévy processes with triplets in a given measurable set \(\Theta\). Under two simple additional conditions on \(\Theta\), they prove that some functional defined by nonlinear expectation can be characterized as the unique viscosity solution of a fully nonlinear partial integro-differential equation which is the analogue of the usual Kolmogorov equation. The given conditions are large enough to allow for unbounded diffusion and infinite variation jumps. As example of such a situation, a nonlinear version of an \(\alpha\)-stable Lévy process is exhibited.