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Journal of Mathematics
Volume 2013, Article ID 640137, 6 pages
http://dx.doi.org/10.1155/2013/640137
Research Article

Functional Limit Theorem for Products of Sums of Independent and Nonidentically Distributed Random Variables

Institute of Mathematics, Maria Curie-Skłodowska University, Plac M.C.-Skłodowskiej 1, 20-031 Lublin, Poland

Received 27 August 2012; Accepted 11 November 2012

Academic Editor: Inés Couso

Copyright © 2013 Przemysław Matuła and Iwona Stępień. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the weak convergence in the space of processes constructed from products of sums of independent but not necessarily identically distributed random variables. The presented results extend and generalize limit theorems known so far for i.i.d. sequences.