Almost sure central limit theorems on the Wiener space

2009/12/12 by Bernard Bercu, Bercu, Bernard, Ivan Nourdin +4
Economics, Econometrics and Finance · Mathematics · #60F05 #60G15 #60H05 #60H07 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.PR #msc:60F05 #msc:60G15 #msc:60H05 #msc:60H07

paper · pdf · doi:10.48550/arxiv.0912.2398

Title changed. Major changes: results improved. 24 pages

arxiv created 2009/12/12 · openalex publication_date 2009/12/12 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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