$G$-martingale representation in the $G$-L'evy setting

Abstract

In this paper we give the decomposition of a martingale under the sublinear expectation associated with a $G$-L'evy process X with finite activity and without drift. We prove that such a martingale consists of an Ito integral w.r.t. continuous part of a $G$-L'evy process, compensated Ito-L'evy integral w.r.t. jump measure associated with $X$ and a non-increasing continuous $G$-martingale starting at 0.

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Cited by in corpus (4)

• Exponential Stability of Solutions to Stochastic Differential Equations Driven by G-Levy Process
• An $\alpha$-stable limit theorem under sublinear expectation
• On the properites of Poisson random measures associated with a G-Levy process
• Path independence of the additive functionals for stochastic differential equations driven by G-Lévy processes