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: 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**0121870**, 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