English

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

Probability 2016-03-25 v1

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.

Keywords

Cite

@article{arxiv.1603.07585,
  title  = {Number of Distinct Sites Visited by a Random Walk with Internal States},
  author = {Péter Nándori},
  journal= {arXiv preprint arXiv:1603.07585},
  year   = {2016}
}