Number of Distinct Sites Visited by a Random Walk with Internal States

Abstract

In the classical paper of Dvoretzky-Erdős, asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit theorem in of Krámli and Szász is also estimated.