Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(5): 1539-1554

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1539

Copyright © The Korean Mathematical Society.

The invariance principle for random sums of a double random sequence

Zhenlong Gao and Liang Fang

Qufu Normal University, Hunan Normal University

Abstract

In this paper, we extend Donsker's invariance principle to the case of random partial sums processes based on a double sequence of row-wise i.i.d. random variables.

Keywords: double random sequence, invariance principle, weak convergence

MSC numbers: 60F05, 60F17