On Regularity and Stability Properties of G-Stochastic Differential Equations with Jumps

This paper deals with a system of G-stochastic differential equations with jumps, driven by G-Brownian motion and G-Lévy process. By using the Burkholdr-Davis-Gundy inequalities, we prove a moment estimate and the temporal Hölder regularity of the solution, under the Linear growth and the global Lipschitz conditions of the coefficients with respect to the state variable uniformly in the time variable. Moreover, different stability properties are proved. Some examples like Black-Scholes market driven by G-Brownian motion are employed in order to support our theoretical results.