基于k-间隔过程的经验过程振动模的强极限
Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process
摘要：
近年来，在iid情形下，人们给出了经验过程振动模的几个强极限定理。我们表明，非常轻微的差异，这些强有力的结果也得到了一些代表性的减少经验过程的基础上（非重叠）的k-间距所产生的序列的独立随机变量（RV的）均匀分布在$(0,1)$。这就产生了上述过程的弱极限。我们的研究包括的情况下，步骤k是无界的。这些结果主要是由关于参数为k和1的Gamma函数增量的几个性质得到的。
英文摘要：
Recently, several strong limit theorems for the oscillation moduli of the empirical process have been given in the iid-case. We show that, with very slight differences, those strong results are also obtained for some representation of the reduced empirical process based on the (non-overlapping) k-spacings generated by a sequence of independent random variables (rv's) uniformly distributed on $(0,1)$. This yields weak limits for the mentioned process. Our study includes the case where the step k is unbounded. The results are mainly derived from several properties concerning the increments of gamma functions with parameters k and one.
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