Some new almost sure results on the functional increments of the uniform empirical process

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• 作者：Davit Varron
• 关键词：Empirical processes ; Functional limit theorems
• 刊名：Stochastic Processes and their Applications
• 出版年：2011
• 出版时间：February 2011
• 年：2011
• 卷：121
• 期：2
• 页码：337-356
• 全文大小：291 K

文摘

Given an observation of the uniform empirical process α_n, its functional increments α_n(u+a_n)−α_n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n→∞ and a_n↓0. Under mild conditions on a_n, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process.