Theoretical and numerical analyses of stabilization of non-linear stochastic differential equations driven by Lévy processes via intermittent feedback controls

Abstract The stabilization of a class of stochastic differential equations by using intermittent feedback control is studied in this paper. The driven noise is taken to be a class of Lévy processes and the drift coefficient is allowed to grow super-linearly. Moreover, numerical analysis of the semi-implicit Euler–Maruyama method that is able to reliably realize such stabilization in the computer simulation is also carried out. Two numerical examples are given to support our theoretical results.