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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multiple points of transient random walks

Author: Joel H. Pitt
Journal: Proc. Amer. Math. Soc. 43 (1974), 195-199
MSC: Primary 60J15
MathSciNet review: 0386021
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Abstract: We determine the asymptotic behavior of the expected numbers of points visited exactly $j$ times and at least $j$ times in the first $n$ steps of a transient random walk on a discrete Abelian group. We prove that the strong law of large numbers holds for these multiple point ranges.

References [Enhancements On Off] (What's this?)

  • A. Dvoretzky and P. Erdös, Some problems on random walk in space, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950., University of California Press, Berkeley and Los Angeles, 1951, pp. 353–367. MR 0047272
  • P. Erdős and S. J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sci. Hungar. 11 (1960), 137–162. (unbound insert) (English, with Russian summary). MR 121870, DOI
  • Frank Spitzer, Principles of random walk, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. MR 0171290

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Keywords: Range of random walk, strong law of large numbers, ergodic theorem
Article copyright: © Copyright 1974 American Mathematical Society