Stationary Solutions for Stochastic Differential Equations Driven by Lévy Processes

In the paper, stationary solutions of stochastic differential equations driven by Lévy processes are considered. And the existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. Moreover, under a one-sided Lipschitz continuity condition and a temperedness condition, Itô and Marcus stochastic differential equations driven by Lévy processes are proved to have stationary solutions. Besides, continuous dependence of stationary solutions on drift coefficients of these equations is presented.