Affiliation:
1. College of Mathematics and Information Science, Henan Normal University
2. College of Mathematics and Statistics, Pingdingshan University
Abstract
In this paper, we consider the following linear process Xn = ?? i=-?
Ci?n-i, n ? Z, and establish the central limit theorem of the randomly
indexed partial sums Svn := X1 +... + Xvn, where {ci,i?Z} is a
sequence of real numbers, {?n,n?Z} is a stationary m-dependent sequence
and {vn;n?1} is a sequence of positive integer valued random variables.
In addition, in order to show the main result, we prove the central limit
theorems for randomly indexed m-dependent random variables, which improve
some known results.
Publisher
National Library of Serbia