Multiple points of transient random walks
Author:
Joel H. Pitt
Journal:
Proc. Amer. Math. Soc. 43 (1974), 195-199
MSC:
Primary 60J15
DOI:
https://doi.org/10.1090/S0002-9939-1974-0386021-0
MathSciNet review:
0386021
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Abstract | References | Similar Articles | Additional Information
Abstract: We determine the asymptotic behavior of the expected numbers of points visited exactly 
times and at least 
times in the first 
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.
- [1] 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
- [2] 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, https://doi.org/10.1007/BF02020631
- [3] 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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0386021-0
Keywords:
Range of random walk,
strong law of large numbers,
ergodic theorem
Article copyright:
© Copyright 1974
American Mathematical Society
