Itô calculus and jump diffusions for $G$-Lévy processes

Abstract

The paper considers the integration theory for $G$-Lévy processes with finite activity. We introduce the Itô-Lévy integrals, give the Itô formula for them and establish SDE's, BSDE's and decoupled FBSDE's driven by $G$-Lévy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a $G$-Lévy process and a characterization of random variables in $L_G^p(\Omega )$ in terms of their quasi-continuity.

References in corpus (4)

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• G-Lévy Processes under Sublinear Expectations
• The Independence under Sublinear Expectations
• On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process

Cited by in corpus (5)

• On the existence-uniqueness and exponential estimate for solutions to stochastic functional differential equations driven by G-Lévy process
• An $\alpha$-stable limit theorem under sublinear expectation
• $G$-martingale representation in the $G$-L'evy setting
• 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