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Number of Distinct Sites Visited by a Random Walk with Internal States
Péter Nándori · 2016-03-24 · via math.PR updates on arXiv.org

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.

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