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January 1998 Wiener's test for random walks with mean zero and finite variance
K\^{o}hei Uchiyama
Ann. Probab. 26(1): 368-376 (January 1998). DOI: 10.1214/aop/1022855424

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 $N \geq 4$.

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K\^{o}hei Uchiyama. "Wiener's test for random walks with mean zero and finite variance." Ann. Probab. 26 (1) 368 - 376, January 1998. https://doi.org/10.1214/aop/1022855424

Information

Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0936.60038
MathSciNet: MR1617054
Digital Object Identifier: 10.1214/aop/1022855424

Subjects:
Primary: 31C20, 60J15, 60J45

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • January 1998
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