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. Dvoretsky and P. Erdös,*Some problems on random walk in space*, Proc. Second Berkeley Sympos. on Math. Statist. and Probability, Univ. of California Press, Berkeley and Los Angeles, 1951, pp. 353-368. MR**13**, 852. MR**0047272 (13:852b)****[2]**P. Erdös and S. J. Taylor,*Some problems concerning the structure of random walk paths*, Acta Math. Acad. Sci. Hungar.**11**(1960), 137-162. MR**22**#12599. MR**0121870 (22:12599)****[3]**F. Spitzer,*Principles of random walk*, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1964. MR**30**#1521. MR**0171290 (30:1521)**

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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