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

Davit Varron

Stochastic Processes and their Applications, 2011, vol. 121, issue 2, 337-356

Abstract: Given an observation of the uniform empirical process [alpha]n, its functional increments [alpha]n(u+an[dot operator])-[alpha]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-->[infinity] and an[downwards arrow]0. Under mild conditions on an, 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.

Keywords: Empirical; processes; Functional; limit; theorems (search for similar items in EconPapers)
Date: 2011
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