The Annals of Probability

Wiener's test for random walks with mean zero and finite variance

K\^{o}hei Uchiyama

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Abstract

It is shown that an infinite subset of $Z^N$ is either recurrent for each aperiodic $N$-dimensional random walk with mean zero and finite variance, or transient for each of such random walks. This is an exact extension of the result by Spitzer in three dimensions to that in the dimensions $N \geq 4$.

Article information

Source
Ann. Probab., Volume 26, Number 1 (1998), 368-376.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855424

Digital Object Identifier
doi:10.1214/aop/1022855424

Mathematical Reviews number (MathSciNet)
MR1617054

Zentralblatt MATH identifier
0936.60038

Subjects
Primary: 60J15 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 31C20: Discrete potential theory and numerical methods

Keywords
Multidimensional random walk Green's function Laplace discrete operator Wiener's test Markov chain transient set

Citation

Uchiyama, K\^{o}hei. Wiener's test for random walks with mean zero and finite variance. Ann. Probab. 26 (1998), no. 1, 368--376. doi:10.1214/aop/1022855424. https://projecteuclid.org/euclid.aop/1022855424


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References

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