We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to measure dependence and allow for additional time dependence. Our main result is a functional central limit theorem for locally stationary processes. Moreover, maximal inequalities for expectations of sums are developed. We show the applicability of our theory in some examples, for instance we provide uniform convergence rates for nonparametric regression with locally stationary noise.

翻译：我们为使用功能依赖性衡量法的当地固定过程的经验过程理论提供了一个框架。我们的结果将固定的Markov链和混合序列的已知结果扩展为另一种常见的可能性,以测量依赖性和允许额外的时间依赖性。我们的主要结果是对当地固定过程的功能中心理论限制。此外,还形成了对金额期望的最大不平等。我们在某些例子中显示了我们理论的适用性,例如,我们为与当地固定噪音的非对称回归提供了统一的趋同率。