SOME RESULTS OF THE INCREMENT OF LOCAL TIME ON A RANDOM WALK

Let N（t） be the local time at zero （the number of returns to zero up to time t） of a reccurrent random walk. We obtain the following main theorem （1） （\lim _x \rightarrow \infty \sup \fracN(T)\sqrtT \log \log T^T=\frac\sqrt2\sigma a.s （2）if \lim _T \rightarrow \infty a_T / \log T=\infty then \beginaligned & \lim _T \rightarrow \infty \sup _a_x