G-Lévy Processes under Sublinear Expectations

Abstract

We introduce G-Lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Lévy-Khintchine formula and the existence for G-Lévy processes. We also introduce G-Poisson processes.

28 pages

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Cited by in corpus (11)

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• $G$-martingale representation in the $G$-L'evy setting
• Convex monotone semigroups on lattices of continuous functions
• On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process
• On the properites of Poisson random measures associated with a G-Levy process
• Martingale Problem under Nonlinear Expectations
• Path independence of the additive functionals for stochastic differential equations driven by G-Lévy processes
• Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity