On the strong mixing property for linear sequences

Let $Z_i$, $i=0,\pm 1,\pm 2,\dots$, be independent random variables and $g_i\in R^1$, $i=0,1,2,\dots$. In the note, sufficient conditions are obtained for the sequence $\displaystyle X_j=\sum_{i=0}^{\infty}g_iZ_{j-i}$ to possess the strong mixing property.