Almost sure central limit theorems on the Wiener space

Bernard Bercu 1, 2, 3 Ivan Nourdin 4 Murad Taqqu 5
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
3 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.
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  • HAL Id : hal-00375290, version 2
  • ARXIV : 0912.2398

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Bernard Bercu, Ivan Nourdin, Murad Taqqu. Almost sure central limit theorems on the Wiener space. Stochastic Processes an their Applications, 2010, 120, pp.1607-1628. ⟨hal-00375290v2⟩

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