2005/10/24 by Magda Peligrad, Peligrad, Magda, Sergey Utev +1
Computer Science · Decision Sciences · Mathematics · #60F05 #60G51 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference #math.PR #msc:60F05 #msc:60G51
paper · pdf · doi:10.48550/arxiv.math/0510513
13 pages. To appear in Stochastic Processes and their Applications
arxiv created 2005/10/24 · openalex publication_date 2005/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Braverman, Mallows and Shepp (1995), showed that if the absolute moments of partial sums of i.i.d. symmetric variables are equal to those of normal variables, then the marginals have normal distribution. This fact suggested the conjecture that probably the absolute moments alone characterize the homogeneous process with independent increments. In this paper we prove a more general result that gives a positive answer to this conjecture, and then apply it in order to obtain the CLT for a class of dependent random variables under a normalization involving the absolute moments of partial sums.