Abstract. We study some properties of the local time of the asymmetric Bernoulli walk on the line. These properties are very similar to the corresponding ones of the simple symmetric random walks in higher ($d\geq3$) dimension, which we established in the recent years. The goal of this paper is to highlight these similarities.

AMS Subject Classification (1991): 60G50; 60F15, 60J55

Keyword(s): transient random walk, local time, occupation time, strong theorems

Received September 21, 2007, and in revised form January 7, 2008. (Registered under 6020/2009.)