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Article Dans Une Revue Stochastic Processes and their Applications Année : 2011

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

Résumé

Given an observation of the uniform empirical process alpha(n) its functional increments alpha(n)(u+a(n).) - 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 a(n) down 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.

Dates et versions

hal-01358246 , version 1 (31-08-2016)

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Citer

Davit Varron. Some new almost sure results on the functional increments of the uniform empirical process. Stochastic Processes and their Applications, 2011, 121 (2), pp.337-356. ⟨10.1016/j.spa.2010.11.006⟩. ⟨hal-01358246⟩
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