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arXiv · 1603.07585

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

Péter Nándori
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Abstract

In the classical paper of Dvoretzky-Erd\H{o}s, 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 Kr\'amli and Sz\'asz is also estimated.

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Péter Nándori. 2016-03-24. Number of Distinct Sites Visited by a Random Walk with Internal States. https://doi.org/10.1007/s00440-010-0277-8

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