Year: 2005
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Peligrad, Magda, Utev, Sergey
Institutions: University of Cincinnati, University of Nottingham
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949101892