Asymptotic Distribution with Random Indices for Linear Processes

In this paper, we consider the following linear process X-n = Sigma C-infinity(i=-infinity)i xi(n-i), n is an element of Z, and establish the central limit theorem of the randomly indexed partial sums S-vn := X-1 + ... + X-vn, where {c(i); i is an element of Z} is a sequence of real numbers, {xi(n); n is an element of Z} is a stationary m-dependent sequence and {v(n); 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.