Asymptotic Stability of stochastic differential equations driven by G-Levy process with delay feedback control

Abstract

Given an unstable stochastic differential equations, the stabilisation by delay feedback controls for such equations under Lipschitz conditions or highly nonlinear conditions have been discussed by several authors. However, there is so far little on the stabilisation by delay feedback controls under the sub-linear expectation associated with a G-L\'{e}vy process. The aim of this paper is to design delay feedback controls in the drift part and obtain the asymptotical stability in mean square and quasi-surely asymptotical stability for the stochastic differential equations driven by G-L\'{e}vy process with the polynomial growth condition. Then we give an example to verify the obtained theory.