Abstract: Let ｛ε^t;t∈Z｝ be a sequence of mdependent Bvalued random elements with mean zeros and finite second moment. ｛a^j; j∈Z｝ is a sequence of real numbers . Define moving average process X^t. Using BeveridgeNelson decomposition and the weak convergence theorem of the sum of ｛ε^t;t≥ 1｝, we studied limit theorem of the sum of ｛X^t;t≥1｝ and gave a sufficient condition of the central limit theorem for the sum of random number of ｛X^t;t≥1｝.

Key words: mdependent random element, moving average process, the central limit theorem for the sum of random numbe