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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


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.


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

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

Primary: 31C20 , 60J15 , 60J45

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

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • January 1998
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