## The Annals of Probability

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

K\^{o}hei Uchiyama

#### 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

https://projecteuclid.org/euclid.aop/1022855424

Digital Object Identifier
doi:10.1214/aop/1022855424

Mathematical Reviews number (MathSciNet)
MR1617054

Zentralblatt MATH identifier
0936.60038

#### 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

#### References

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