La convergence complète de processus moyenne mobile.

Abstract

The main purpose of this text is to study the complete convergence for moving average processes defined thus Xn = +X1 j=0 cn+jYj Where (Yj)j2Z is a two sieled infinite sequence of negative dependent sub-gaussian random variables and (cj)j2Z is an absolutely summable sequence of real numbers. In this work, we have developed the results obtained by Amini Dehak, Mohammad, Nili Sani, H.R. et Bozorgnia, A in their articles [1] which have proved that this processes are sub-gaussian random variables with (Xn) Moreover if (Yj)j2Z is a doubly infinite sequence of negative dependent random variable dominated by Y such that Y is a sub-gaussian random variable with (Y ) under suitable conditions on the sequence (cj)j2Z, then all of the above theorems and lemmas remain true.