Abstract. In this paper, an almost sure central limit theorem is obtained for self-normalized weighted sums of the φ mixing random variables. Our results extend and give substantial improvement for the result obtained by Zhang [12] and our results also extend the earlier work on almost sure central limit theorem such as Wu [13].Mathematics subject classification (2010): 60F15.

Abstract. In this paper, we establish complete convergence results and a complete moment convergence result and prove the equivalence of them for weighted sums ofρ -mixing random variables. Our results generalize and improve the results of Baum and Katz(1965) and Peligrad and Gut (1999). As an application, we obtain the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums ofρ -mixing random variables.Mathematics subject classification (2010): 60F15.