We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type results under different observation schemes. Hereditary properties for a large class of finite and infinite memory transformations show the flexibility of the developed theory. Sufficient conditions for the existence of stationary approximations for time-varying L\'evy-driven state space models are derived and compared to existing results. We conclude with comprehensive results on the asymptotic behavior of the first and second order localized sample moments of time-varying L\'evy-driven state space models.

翻译：我们引入了当地固定连续时间过程的固定近似值的一般理论。 根据固定近似值,我们使用 $\theta$-weak 依赖度来确定不同观测计划下大量数量和中央限值类型结果的法律。 大量有限和无限记忆转换的遗传属性显示了发达理论的灵活性。 得出并比较了时间变化L\'evy驱动的状态空间模型的固定近近近值的充足条件。 我们最后得出了第一和第二顺序局部抽样时间变化L\'evy驱动的状态空间模型无症状行为的全面结果。