Another approach to Brownian motion
Probability
2007-05-23 v1
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.
Cite
@article{arxiv.math/0510513,
title = {Another approach to Brownian motion},
author = {Magda Peligrad and Sergey Utev},
journal= {arXiv preprint arXiv:math/0510513},
year = {2007}
}
Comments
13 pages. To appear in Stochastic Processes and their Applications