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Number of distinct sites visited by a random walk with internal states
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  • Published: 11 March 2010

Number of distinct sites visited by a random walk with internal states

  • Péter Nándori1 

Probability Theory and Related Fields volume 150, pages 373–403 (2011)Cite this article

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Abstract

In the classical paper of Dvoretzky and Erdős (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951), 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 Krámli and Szász (Zeitschrift Wahrscheinlichkeitstheorie verw Gebiete 63:85–95, 1983) is also estimated.

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Authors and Affiliations

  1. Institute of Mathematics, Budapest University of Technology and Economics, Egry József u. 1., Budapest, 1111, Hungary

    Péter Nándori

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  1. Péter Nándori
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Correspondence to Péter Nándori.

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Nándori, P. Number of distinct sites visited by a random walk with internal states. Probab. Theory Relat. Fields 150, 373–403 (2011). https://doi.org/10.1007/s00440-010-0277-8

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  • Received: 01 September 2009

  • Revised: 04 February 2010

  • Published: 11 March 2010

  • Issue Date: August 2011

  • DOI: https://doi.org/10.1007/s00440-010-0277-8

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Keywords

  • Random walk with internal states
  • Markov chain
  • Visited points
  • Local limit theorem
  • Law of large numbers

Mathematics Subject Classification (2000)

  • 60J10
  • 82C41
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